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Academic literature on the topic 'Algebra, Abstract'

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Published: 4 June 2021

Last updated: 31 July 2024

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Journal articles on the topic "Algebra, Abstract"

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Sreeja S Nair, Kumari. "Exploring Normal Covering Spaces: A Bridge between Algebraic Topology and Abstract Algebra." International Journal of Science and Research (IJSR) 12, no. 8 (August 5, 2023): 2474–77. http://dx.doi.org/10.21275/sr23824225856.

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SAMEA, H. "ESSENTIAL AMENABILITY OF ABSTRACT SEGAL ALGEBRAS." Bulletin of the Australian Mathematical Society 79, no. 2 (March 13, 2009): 319–25. http://dx.doi.org/10.1017/s0004972708001329.

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AbstractA number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.

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Chen, Quanguo, and Yong Deng. "Hopf algebra structures on generalized quaternion algebras." Electronic Research Archive 32, no. 5 (2024): 3334–62. http://dx.doi.org/10.3934/era.2024154.

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<abstract><p>In this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given. It is proven that not all of the generalized quaternion algebras have Hopf algebraic structures. When the generalized quaternion algebras have Hopf algebraic structures, we describe all the Hopf algebra structures. Finally, we shall prove that all the Hopf algebra structures on the generalized quaternion algebras are isomorphic to Sweedler Hopf algebra, which is consistent with the classification of 4-dimensional Hopf algebras.</p></abstract>

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Benkart, Georgia, and I. N. Herstein. "Abstract Algebra." American Mathematical Monthly 94, no. 8 (October 1987): 804. http://dx.doi.org/10.2307/2323434.

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Freedman, Haya, G. D. Crown, M. H. Fenrick, and R. J. Valenza. "Abstract Algebra." Mathematical Gazette 71, no. 455 (March 1987): 89. http://dx.doi.org/10.2307/3616329.

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Madden, Daniel J., Ronald Solomon, and Ronald S. Irving. "Abstract Algebra." American Mathematical Monthly 112, no. 5 (May 1, 2005): 475. http://dx.doi.org/10.2307/30037513.

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7

Sharma, Vibhuti. "Abstract Algebra." International Journal for Research in Applied Science and Engineering Technology 9, no. VII (July 20, 2021): 1628–34. http://dx.doi.org/10.22214/ijraset.2021.36688.

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Ring hypothesis is one of the pieces of the theoretical polynomial math that has been thoroughly used in pictures. Nevertheless, ring hypothesis has not been associated with picture division. In this paper, we propose another rundown of similarity among pictures using rings and the entropy work. This new record was associated as another stopping standard to the Mean Shift Iterative Calculation with the goal to accomplish a predominant division. An examination on the execution of the calculation with this new ending standard is finished. In spite of the fact that ring hypothesis and class hypothesis from the start sought after assorted direction it turned out during the 1970s – that the investigation of functor groupings furthermore reveals new plots for module hypothesis.

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Bai, Liqian, Xueqing Chen, Ming Ding, and Fan Xu. "A generalized quantum cluster algebra of Kronecker type." Electronic Research Archive 32, no. 1 (2024): 670–85. http://dx.doi.org/10.3934/era.2024032.

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<abstract><p>The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra.</p></abstract>

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9

Huang, Junyuan, Xueqing Chen, Zhiqi Chen, and Ming Ding. "On a conjecture on transposed Poisson $ n $-Lie algebras." AIMS Mathematics 9, no. 3 (2024): 6709–33. http://dx.doi.org/10.3934/math.2024327.

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<abstract><p>The notion of a transposed Poisson $ n $-Lie algebra has been developed as a natural generalization of a transposed Poisson algebra. It was conjectured that a transposed Poisson $ n $-Lie algebra with a derivation gives rise to a transposed Poisson $ (n+1) $-Lie algebra. In this paper, we focus on transposed Poisson $ n $-Lie algebras. We have obtained a rich family of identities for these algebras. As an application of these formulas, we provide a construction of $ (n+1) $-Lie algebras from transposed Poisson $ n $-Lie algebras with derivations under a certain strong condition, and we prove the conjecture in these cases.</p></abstract>

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Bezhanishvili, Guram, and Patrick J. Morandi. "Profinite Heyting Algebras and Profinite Completions of Heyting Algebras." gmj 16, no. 1 (March 2009): 29–47. http://dx.doi.org/10.1515/gmj.2009.29.

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Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.

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Dissertations / Theses on the topic "Algebra, Abstract"

1

Frisk, Anders. "On the structure of standardly stratified algebras /." Uppsala, 2004. http://www.math.uu.se/research/pub/Frisk5lic.pdf.

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Wiesnet, Franziskus Wolfgang Josef. "The computational content of abstract algebra and analysis." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/313875.

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In this dissertation we discuss several forms of proof interpretation based on examples in algebra and analysis. Our main goal is the construction of algorithms or functions out of proofs - constructive proofs and classical proofs. At the beginning of this dissertation the constructive handling of Zorn's lemma in proofs of algebra plays a main role. We consider maximal objects and their approximations in various algebraic structures. The approximation is inspired by Gödel's functional interpretation and methods from proof mining. Proof mining is a branch of mathematical logic which analyses classical existence statements to get explicit bounds. We describe a recursive algorithm which constructs a sequence of approximations until they become close enough. This algorithm will be applied to Krull's lemma and its generalisation: the universal Krull-Lindenbaum lemma. In some case studies and applications like the theorem of Gauß-Joyal and Kronecker's theorem we show explicit uses of this algorithm. By considering Zariski's lemma we present how a manual construction of an algorithm from a constructive proof works. We formulate a constructive proof of Zariski's lemma, and use this proof as inspiration to formulate an algorithm and a computational interpretation of Zariski's lemma. Finally, we prove that the algorithm indeed fulfils the computational interpretation. As an outlook we sketch how this algorithm could be combined with our state-based algorithm from above which constructs approximations of maximal objects, to get an algorithm for Hilbert's Nullstellensatz. We then take a closer look at an example of an algorithm which is extracted out of a constructive proof by using a computer assistant. In our case we use the proof assistant Minlog. We use coinductively defined predicates to prove that the signed digit representation of real numbers is closed under limits of convergent sequences. From a formal proof in Minlog, the computer generates an algorithm, a soundness theorem and a proof of the soundness theorem corresponding to the convergence theorem out of our formalisation. The convergence theorem is applied to Heron's method to get an algorithm which computes the signed digit representation of the square root of a non-negative real number out of its signed digit representation. Here we use the programming language Haskell to display the computational content. As second application we show that the signed digit code is closed under multiplication and state the corresponding algorithm. This dissertation is concluded by an example of proof mining in analysis. We consider one convergence lemma with a classical proof, use techniques of proof mining to get a new lemma with a rate of convergence, and apply the new lemma to various fixed-point theorems for asymptotically weakly contractive maps and their variants. In the last step, beside extracting quantitative information - in our case rates of convergence - from proofs, we also discuss the usage of proof mining to generalise or combine theorems.

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Wiesnet, Franziskus Wolfgang Josef. "The computational content of abstract algebra and analysis." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/313875.

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In this dissertation we discuss several forms of proof interpretation based on examples in algebra and analysis. Our main goal is the construction of algorithms or functions out of proofs - constructive proofs and classical proofs. At the beginning of this dissertation the constructive handling of Zorn's lemma in proofs of algebra plays a main role. We consider maximal objects and their approximations in various algebraic structures. The approximation is inspired by Gödel's functional interpretation and methods from proof mining. Proof mining is a branch of mathematical logic which analyses classical existence statements to get explicit bounds. We describe a recursive algorithm which constructs a sequence of approximations until they become close enough. This algorithm will be applied to Krull's lemma and its generalisation: the universal Krull-Lindenbaum lemma. In some case studies and applications like the theorem of Gauß-Joyal and Kronecker's theorem we show explicit uses of this algorithm. By considering Zariski's lemma we present how a manual construction of an algorithm from a constructive proof works. We formulate a constructive proof of Zariski's lemma, and use this proof as inspiration to formulate an algorithm and a computational interpretation of Zariski's lemma. Finally, we prove that the algorithm indeed fulfils the computational interpretation. As an outlook we sketch how this algorithm could be combined with our state-based algorithm from above which constructs approximations of maximal objects, to get an algorithm for Hilbert's Nullstellensatz. We then take a closer look at an example of an algorithm which is extracted out of a constructive proof by using a computer assistant. In our case we use the proof assistant Minlog. We use coinductively defined predicates to prove that the signed digit representation of real numbers is closed under limits of convergent sequences. From a formal proof in Minlog, the computer generates an algorithm, a soundness theorem and a proof of the soundness theorem corresponding to the convergence theorem out of our formalisation. The convergence theorem is applied to Heron's method to get an algorithm which computes the signed digit representation of the square root of a non-negative real number out of its signed digit representation. Here we use the programming language Haskell to display the computational content. As second application we show that the signed digit code is closed under multiplication and state the corresponding algorithm. This dissertation is concluded by an example of proof mining in analysis. We consider one convergence lemma with a classical proof, use techniques of proof mining to get a new lemma with a rate of convergence, and apply the new lemma to various fixed-point theorems for asymptotically weakly contractive maps and their variants. In the last step, beside extracting quantitative information - in our case rates of convergence - from proofs, we also discuss the usage of proof mining to generalise or combine theorems.

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Juett, Jason Robert. "Some topics in abstract factorization." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2534.

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Anderson and Frazier defined a generalization of factorization in integral domains called tau-factorization. If D is an integral domain and tau is a symmetric relation on the nonzero nonunits of D, then a tau-factorization of a nonzero nonunit a in D is an expression a = lambda a_1 ... a_n, where lambda is a unit in D, each a_i is a nonzero nonunit in D, and a_i tau a_j for i != j. If tau = D^# x D^#, where D^# denotes the nonzero nonunits of D, then the tau-factorizations are just the usual factorizations, and with other choices of tau we get interesting variants on standard factorization. For example, if we define a tau_d b if and only if (a, b) = D, then the tau_d-factorizations are the comaximal factorizations introduced by McAdam and Swan. Anderson and Frazier defined tau-factorization analogues of many different factorization concepts and properties, and proved a number of theorems either generalizing standard factorization results or the comaximal factorization results of McAdam and Swan. Some of these concepts include tau-UFD's, tau-atomic domains, the tau-ACCP property, tau-BFD's, tau-FFD's, and tau-HFD's. They showed the implications between these concepts and showed how each of the standard variations implied their tau-factorization counterparts (sometimes assuming certain natural constraints on tau). Later, Ortiz-Albino introduced a new concept called Gamma-factorization that generalized tau-factorization. We will summarize the known theory of tau-factorization and Gamma-factorization as well as introduce several new or improved results.

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Fernandes, Renato da Silva. "Combinatória: dos princípios fundamentais da contagem à álgebra abstrata." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-31012018-161438/.

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O objetivo deste trabalho é fazer um estudo amplo e sequencial sobre combinatória. Iniciase com os fundamentos da combinatória enumerativa, tais como permutações, combinações simples, combinações completas e os lemas de Kaplanski. Num segundo momento é apresentado uma abordagem aos problemas de contagem utilizando a teoria de conjuntos; são abordados o princípio da inclusão-exclusão, permutações caóticas e a contagem de funções. No terceiro momento é feito um aprofundamento do conceito de permutação sob a ótica da álgebra abstrata. É explorado o conceito de grupo de permutações e resultados importantes relacionados. Na sequência propõe-se uma relação de ordem completa e estrita para o grupo de permutações. Por fim, investiga-se dois problemas interessantes da combinatória: a determinação do número de caminhos numa malha quadriculada e a contagem de permutações que desconhecem padrões de comprimento três.
The objective of this work is to make a broad and sequential study on combinatorics. It begins with the foundations of enumerative combinatorics, such as permutations, simple combinations, complete combinations, and Kaplanskis lemmas. In a second moment an approach is presented to the counting problems using set theory; the principle of inclusion-exclusion, chaotic permutations and the counting of functions are addressed. In the third moment a deepening of the concept of permutation is made from the perspective of abstract algebra. The concept of group of permutations and related important results is explored. A strict total order relation for the permutation group is proposed. Finally, we investigate two interesting combinatorial problems: the determination of the number of paths in a grid and the number of permutations that avoids patterns of length three.

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Awuah, Bernard Prince. "The effectiveness of the concrete / semi-concrete / abstract (CSA) appoach and drill- practice on grade 10 learners' ability to simplify addition and subtraction algebraic fractions." Thesis, University of Fort Hare, 2016. http://hdl.handle.net/10353/5105.

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This study was conducted in one of the education districts in the Eastern Cape Province of South Africa. The purpose was to analyse the effectiveness of the concrete/semi-concrete/abstract (CSA) approach and drill-practice instructional strategies on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. The following two objectives were set. First, to identify the learners’ challenges in studying addition and subtraction of algebraic fractions in grade 10; and second to analyse the effectiveness of the CSA approach and drill-practice instructional strategies on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. Both threshold concepts and troublesome knowledge, Polya’s problem-solving techniques, CSA Approach theory and Drill-practice theory were all pertinent as a theoretical framework for the study. Positivism research paradigm was adopted for the study and it afforded the researcher opportunity to employ quantitative research approach. Based on the research question of this study, an experimental design was chosen as a suitable descriptive design. Purposive sampling method was used to select three schools which involved 135 grade 10 mathematics learners. Stratified random sampling method was thereafter employed to select 45 learners from each school for the study. The learners were grouped in each school as top, average and weak based on their performance in Algebra in term one. Pre-questionnaire and post-questionnaire were used to obtain data regarding challenges learners experience in simplifying addition and subtraction of algebraic fractions. Ethical clearance from the relevant school and university authorities were obtained. On the first two days, the researcher briefed the school authorities and learners and explained to them the purpose and details of the study. Day three was used to administer the pre-questionnaire test, thereafter, the next ten days were used to teach addition and subtraction of both numeric and algebraic fractions with same and different numerators and denominators. The next two days were used for revision and the last day was used to administer the postquestionnaire test out 25 marks. The respondent rate was 98.5%. The data collected were analysed by using SPSS version 16.10. Both descriptive and inferential statistics were used to analyse the data. The pre-questionnaire scores revealed that majority of the learners’ perceived fractions as two separate entities and as a result add or subtract numerator to numerator and denominator to denominator. It was also discovered that learners had a challenge in finding LCM of algebraic fractions. A t-Test for independent means was used to test the following hypotheses at 𝛼 = 0.05: 𝐇𝟎: The CSA approach and drill-practice intervention has no significant effect on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions; 𝐇𝟏: The CSA approach and drill-practice will significantly enhance Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. The t-Test revealed a p-value of 0.139 which was statistically significant at 𝛼 = 0.05. Therefore, the researcher rejected the null hypothesis and concluded that the CSA approach and drill-practice have significantly enhanced the Grade 10 learners’ ability to simplify algebraic fractions.

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Rome, Zachary Robert. "Computational Abstract Algebra: Using Monomial Matrices to Represent Groups in GAP." Thesis, The University of Arizona, 2012. http://hdl.handle.net/10150/244772.

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A monomial matrix is a matrix with exactly one non-zero element in each row and column. We will utilize GAP to construct all (transitive) representations of a given group using monomial matrices. First, essential group theory definitions and theorems will be provided, as well as an in-depth look at table of marks and monomial matrices. After describing the necessary mathematics, we will explore the GAP programming needed to achieve this goal. Ultimately we want a table, where each row represents a subgroup of the given group and, within the row, the table will hold the linear characters fixed by the monomial matrices of that subgroup. We will furthermore explore how to represent monomial matrices computationally in different ways and how to create a data structure to represent them. Our final goal will require GAP functions for finding all homomorphisms from a subgroup to roots of unity, using these homomorphisms to create monomial matrix representations of the group, and iterating through the subgroups of the group (up to conjugacy) to find all (transitive) monomial matrix representations of the group.

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Ahlgren, Joyce Christine. "Ideals, varieties, and Groebner bases." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2282.

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The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.

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SPINOSA, Leonardo. "Burnside and Mackey Theories for Abstract Groupoids." Doctoral thesis, Università degli studi di Ferrara, 2019. http://hdl.handle.net/11392/2488082.

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The objective of this thesis is the study of Burnside and Mackey theories for abstract groupoids, which are natural generalizations of groups. In fact, a groupoid can be thought as a group with many objects. In Chapter 1 we will start explaining the basic properties of groupoids and after that, we will prove some properties of the two monoidal structures on the category of groupoid-sets (generalizations of group-sets). Namely, the structure given by the coproduct, that is, the disjoint union, and the other one given by the fibre product over the set of objects of the groupoid, considered canonically as a groupoid-set. In Chapter 2 we will develop a theory of conjugations for subgroupoids, showing the deep differences with the group case. Moreover, we will use this theory to prove a version of the Burnside Theorem for groupoids, with the appropriate finiteness hypotheses. In Chapter 3 we will prove a version of the famous Mackey formula for group-bisets in the case of groupoid-bisets, showing its efficacy with a specific example. In Chapter 4 we will discuss the equivalence of two groupoids as categories and what this implies for the groupoid-biset categories involved. In Chapter 5, following the classical path, we will develop a Burnside theory for groupoids, showing that the Burnside ring of a groupoid is isomorphic to the direct product of the Burnside rings of its isotropy group types. This puts in evidence that the classical methods only lead to the study of a part of the poset of subgroupoids, as the subgroupoids with several objects don't show up. In Chapter 6 we will develop a categorification of the classical notion of groupoid-set, replacing it with an internal category in the category of groupoid-sets, called a categorified groupoid-set. Subsequently, we will use this notion to construct a new Burnside theory for groupoids and we will finish showing that, even in this case, the categorified Burnside ring of a groupoid is isomorphic to the direct product of the categorified Burnside rings of its isotropy group types. This makes manifest that the study of groupoids needs more sophisticated tools and techniques than the traditional ones. In the appendixes we will explain how to pass from a rig (also called semiring), that is, a ring without additive inverses, to a ring, using a construction called Grothendieck functor. This notion is crucial to both the Burnside theories we developed. Moreover, in the last appendix we will collect some definitions about monoidal categories, to fix the employed terminology, and we will prove a known result on monoidal functors whose whole proof we have been unable to find elsewhere.
L'obiettivo di questa tesi è lo studio delle teorie di Mackey e Burnside per i gruppoidi astratti, che sono generalizzazioni naturali dei gruppi. Infatti, un gruppoide può essere pensato come un gruppo con molti oggetti. Nel Capitolo 1 verranno innanzitutto illustrate le proprietà basilari dei gruppoidi; successivamente, verranno provate alcune proprietà delle due strutture monoidali sulla categoria dei groupoid-set (generalizzazioni dei group-set). Per la precisione, la struttura data dal coprodotto, cioè l'unione disgiunta, e la struttura data dal prodotto fibrato sull'insieme degli oggetti del gruppoide, considerato in modo canonico come un groupoid-set. Nel Capitolo 2 verrà sviluppata una teoria delle coniugazioni per i sottogruppoidi, mostrando le profonde differenze con il caso dei gruppi. Inoltre, questa teoria verrà utilizzata per provare una versione del teorema di Burnside per i gruppoidi, con le appropriate ipotesi di finitezza. Nel Capitolo 3 verrà provata una versione della famosa formula di Mackey per i group-biset nel caso dei groupoid-biset, mostrando la sua efficacia con uno specifico esempio. Nel Capitolo 4 verrà discussa l'equivalenza di due gruppoidi come categorie e cosa questo implichi per le categorie di groupoid-biset coinvolte. Nel Capitolo 5, seguendo la teoria classica, verrà sviluppata una teoria di Burnside per i gruppoidi, mostrando come l'anello di Burnside di un gruppoide sia isomorfo al prodotto diretto degli anelli di Burnside dei suoi gruppi di isotropia, uno per ogni componente connessa. Tutto ciò dimostra chiaramente come i metodi classici conducano allo studio solamente di una parte del poset dei sottogruppoidi, dato che i sottogruppoidi con più di un oggetto non compaiono. Nel Capitolo 6 verrà sviluppata una categorificazione della classica nozione di groupoid-set, sostituendolo con una categoria interna alla categoria dei groupoid-set, chiamata un groupoid-set categorificato. Successivamente, questa nozione verrà utilizzata per costruire una nuova teoria di Burnside per i gruppoidi e, infine, verrà dimostrato come, anche in questo caso, l'anello di Burnside categorificato di un gruppoide sia isomorfo al prodotto diretto degli anelli di Burnside categorificati dei suoi gruppi di isotropia, uno per ogni componente connessa. Tutto ciò dimostra come lo studio dei gruppoidi necessiti di tecniche e strumenti più sofisticati di quelli tradizionali. Nelle appendici verrà spiegato come passare da un rig (chiamato anche semianello), cioè un anello privo degli inversi additivi, a un anello, usando una costruzione chiamata funtore di Grothendieck. Questa nozione è cruciale per entrambe le teorie di Burnside sviluppate in questa tesi. Inoltre, nell'ultima appendice verranno riunite alcune definizioni sulle categorie monoidali, per fissare la terminologia utilizzata, e verrà provato un risultato conosciuto del quale, però, non si riesce a trovare altrove la dimostrazione.

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Vernitski, Alexei. "Classes of abstract semigroups closed under the formation of subsemigroups and finitary direct products." Thesis, University of Essex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284611.

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Books on the topic "Algebra, Abstract"

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1950-, Foote Richard M., ed. Abstract algebra. 3rd ed. Hoboken, NJ: Wiley, 2004.

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Dummit, David Steven. Abstract algebra. Englewood Cliffs, N.J: Prentice Hall, 1991.

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Dummit, David Steven. Abstract algebra. 2nd ed. Upper Saddle River, N.J: Prentice Hall, 1999.

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Dummit, David Steven. Abstract Algebra. Hoboken, NJ: Wiley, 2004.

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Deskins, W. E. Abstract algebra. New York: Dover Publications, 1995.

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Herstein, I. N. Abstract algebra. 3rd ed. Upper Saddle River, N.J: Prentice-Hall, 1996.

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Durbin, John R. Modern algebra: An introduction. 3rd ed. New York, NY: Wiley, 1992.

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1948-, Fine Benjamin, and Rosenberger Gerhard, eds. Abstract algebra. Berlin: De Gruyter, 2011.

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Durbin, John R. Modern algebra: An introduction. 2nd ed. New York: Wiley, 1985.

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Paulsen, William. Abstract Algebra. 2nd edition. | Boca Raton : Taylor & Francis, 2016. | Series: Textbooks in mathematics ; 40 | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315370972.

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Book chapters on the topic "Algebra, Abstract"

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Rubinstein-Salzedo, Simon. "Abstract Algebra." In Springer Undergraduate Mathematics Series, 85–87. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94818-8_9.

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Finston, David R., and Patrick J. Morandi. "Identification Numbers and Modular Arithmetic." In Abstract Algebra, 1–21. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_1.

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Finston, David R., and Patrick J. Morandi. "Symmetry." In Abstract Algebra, 145–81. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_10.

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Finston, David R., and Patrick J. Morandi. "Correction to: Identification Numbers and Modular Arithmetic." In Abstract Algebra, C1. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-04498-9_11.

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Finston, David R., and Patrick J. Morandi. "Error Correcting Codes." In Abstract Algebra, 23–40. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_2.

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Finston, David R., and Patrick J. Morandi. "Rings and Fields." In Abstract Algebra, 41–55. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_3.

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Finston, David R., and Patrick J. Morandi. "Linear Algebra and Linear Codes." In Abstract Algebra, 57–72. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_4.

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Finston, David R., and Patrick J. Morandi. "Quotient Rings and Field Extensions." In Abstract Algebra, 73–91. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_5.

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Finston, David R., and Patrick J. Morandi. "Ruler and Compass Constructions." In Abstract Algebra, 93–104. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_6.

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Finston, David R., and Patrick J. Morandi. "Cyclic Codes." In Abstract Algebra, 105–20. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_7.

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Conference papers on the topic "Algebra, Abstract"

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Wang, Yingxu. "On Abstract Systems and System Algebra." In 2006 5th IEEE International Conference on Cognitive Informatics. IEEE, 2006. http://dx.doi.org/10.1109/coginf.2006.365515.

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Chen, Xinzuo. "Core of abstract algebra: group theory." In 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), edited by Chi-Hua Chen, Xuexia Ye, and Hari Mohan Srivastava. SPIE, 2022. http://dx.doi.org/10.1117/12.2639400.

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Santas, Phillip S. "A type system for computer algebra (abstract)." In the 1993 international symposium. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/164081.164096.

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Risnanosanti and Yuriska Destania. "Undergraduate Students’ Conceptual Understanding on Abstract Algebra." In International Conference on Mathematics and Islam. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0008523304380443.

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Hasan Shaheed, Hassnaa, Judy-anne Osborn, and Malcolm Roberts. "Modelling the diversity of Tertiary Abstract Algebra Textbooks." In International Conference on Research in Teaching and Education. Acavent, 2019. http://dx.doi.org/10.33422/rteconf.2019.06.339.

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NEUMANN, ERIC K., SVETLANA LOCKWOOD, BALA KRISHNAMOORTHY, and DAVID SPIVAK. "WORKSHOP ON TOPOLOGY AND ABSTRACT ALGEBRA FOR BIOMEDICINE." In Proceedings of the Pacific Symposium. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814749411_0053.

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Yufeng Wang. "A Systematical Natural Language Model by Abstract Algebra." In 2007 IEEE International Conference on Control and Automation. IEEE, 2007. http://dx.doi.org/10.1109/icca.2007.4376566.

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Freudenthal, Eric A., Kien Lim, Karla Carmona, and Catherine Tabor. "Integrating Programming into Physics and Algebra (Abstract Only)." In SIGCSE '15: The 46th ACM Technical Symposium on Computer Science Education. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2676723.2691884.

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Tomé Cortiñas, Carlos, and Wouter Swierstra. "From algebra to abstract machine: a verified generic construction." In ICFP '18: 23nd ACM SIGPLAN International Conference on Functional Programming. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3240719.3241787.

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Abraham, Erika. "Abstract domains in SMT solving for real algebra (invited talk)." In SPLASH '20: Conference on Systems, Programming, Languages, and Applications, Software for Humanity. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3427762.3430180.

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Reports on the topic "Algebra, Abstract"

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Aadithya, Karthik, Eric Keiter, and Ting Mei. Abstract Algebra Basics. Office of Scientific and Technical Information (OSTI), March 2019. http://dx.doi.org/10.2172/1761970.

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Bardzell, Mike, Jennifer Bergner, Kathleen Shannon, Don Spickler, and Tyler Evans. PascGalois Abstract Algebra Classroom Resources. Washington, DC: The MAA Mathematical Sciences Digital Library, July 2008. http://dx.doi.org/10.4169/loci002636.

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Barnett, Janet Heine. Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization. Washington, DC: The MAA Mathematical Sciences Digital Library, July 2013. http://dx.doi.org/10.4169/loci003998.

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Sixth SIAM conference on applied linear algebra: Final program and abstracts. Final technical report. Office of Scientific and Technical Information (OSTI), December 1997. http://dx.doi.org/10.2172/674876.

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