Relevant bibliographies by topics / Commutative ring

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Commutative ring'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Commutative ring"

1

Abdurrazzaq, Achmad, Ari Wardayani, and Suroto Suroto. "RING MATRIKS ATAS RING KOMUTATIF." Jurnal Ilmiah Matematika dan Pendidikan Matematika 7, no. 1 (June 26, 2015): 11. http://dx.doi.org/10.20884/1.jmp.2015.7.1.2895.

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This paper discusses a matrices over a commutative ring. A matrices over commutative rings is a matrices whose entries are the elements of the commutative ring. We investigates the structure of the set of the matrices over the commutative ring. We obtain that the set of the matrices over the commutative ring equipped with an addition and a multiplication operation of matrices is a ring with a unit element.
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Andruszkiewicz, R. R., and E. R. Puczyłowski. "On commutative idempotent rings." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 2 (1995): 341–49. http://dx.doi.org/10.1017/s0308210500028067.

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We study the problem when a ring which is an extension of a commutative idempotent ring by a commutative idempotent ring is commutative. In particular, we answer Sands' question showing that the class of commutative idempotent rings whose every homomorphic image has zero annihilator is a maximal but not the largest radical class consisting of commutative idempotent rings.
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PENK, TOMÁŠ, and JAN ŽEMLIČKA. "COMMUTATIVE TALL RINGS." Journal of Algebra and Its Applications 13, no. 04 (January 9, 2014): 1350129. http://dx.doi.org/10.1142/s0219498813501296.

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A ring is right tall if every non-noetherian right module contains a proper non-noetherian submodule. We prove a ring-theoretical criterion of tall commutative rings. Besides other examples which illustrate limits of proven necessary and sufficient conditions, we construct an example of a tall commutative ring that is non-max.
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ALHEVAZ, A., and D. KIANI. "McCOY PROPERTY OF SKEW LAURENT POLYNOMIALS AND POWER SERIES RINGS." Journal of Algebra and Its Applications 13, no. 02 (October 10, 2013): 1350083. http://dx.doi.org/10.1142/s0219498813500837.

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One of the important properties of commutative rings, proved by McCoy [Remarks on divisors of zero, Amer. Math. Monthly49(5) (1942) 286–295], is that if two nonzero polynomials annihilate each other over a commutative ring then each polynomial has a nonzero annihilator in the base ring. Nielsen [Semi-commutativity and the McCoy condition, J. Algebra298(1) (2006) 134–141] generalizes this property to non-commutative rings. Let M be a monoid and σ be an automorphism of a ring R. For the continuation of McCoy property of non-commutative rings, in this paper, we extend the McCoy's theorem to skew Laurent power series ring R[[x, x-1; σ]] and skew monoid ring R * M over general non-commutative rings. Constructing various examples, we classify how these skew versions of McCoy property behaves under various ring extensions. Moreover, we investigate relations between these properties and other standard ring-theoretic properties such as zip rings and rings with Property (A). As a consequence we extend and unify several known results related to McCoy rings.
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Alhevaz, Abdollah, Ebrahim Hashemi, and Rasul Mohammadi. "On transfer of annihilator conditions of rings." Journal of Algebra and Its Applications 17, no. 10 (October 2018): 1850199. http://dx.doi.org/10.1142/s0219498818501992.

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It is well known that a polynomial [Formula: see text] over a commutative ring [Formula: see text] with identity is a zero-divisor in [Formula: see text] if and only if [Formula: see text] has a non-zero annihilator in the base ring, where [Formula: see text] is the polynomial ring with indeterminate [Formula: see text] over [Formula: see text]. But this result fails in non-commutative rings and in the case of formal power series ring. In this paper, we consider the problem of determining some annihilator properties of the formal power series ring [Formula: see text] over an associative non-commutative ring [Formula: see text]. We investigate relations between power series-wise McCoy property and other standard ring-theoretic properties. In this context, we consider right zip rings, right strongly [Formula: see text] rings and rings with right Property [Formula: see text]. We give a generalization (in the case of non-commutative ring) of a classical results related to the annihilator of formal power series rings over the commutative Noetherian rings. We also give a partial answer, in the case of formal power series ring, to the question posed in [1 Question, p. 16].
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Ying, Zhiling, and Jianlong Chen. "On Quasipolar Rings." Algebra Colloquium 19, no. 04 (October 15, 2012): 683–92. http://dx.doi.org/10.1142/s1005386712000557.

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The notion of quasipolar elements of rings was introduced by Koliha and Patricio in 2002. In this paper, we introduce the notion of quasipolar rings and relate it to other familiar notions in ring theory. It is proved that both strongly π-regular rings and uniquely clean rings are quasipolar, and quasipolar rings are strongly clean, but no two of these classes of rings are equivalent. For commutative rings, quasipolar rings coincide with semiregular rings. It is also proved that every n × n upper triangular matrix ring over any commutative uniquely clean ring or commutative local ring is quasipolar.
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Al Khalaf, Ahmad, Orest D. Artemovych, and Iman Taha. "Derivations in differentially prime rings." Journal of Algebra and Its Applications 17, no. 07 (June 13, 2018): 1850129. http://dx.doi.org/10.1142/s0219498818501293.

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Earlier properties of Lie rings [Formula: see text] of derivations in commutative differentially prime rings [Formula: see text] was investigated by many authors. We study Lie rings [Formula: see text] in the non-commutative case and shown that if [Formula: see text] is a [Formula: see text]-prime ring of characteristic [Formula: see text], then [Formula: see text] is a prime Lie ring or [Formula: see text] is a commutative ring.
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Lawson, Tyler. "Commutative Γ-rings do not model all commutative ring spectra." Homology, Homotopy and Applications 11, no. 2 (2009): 189–94. http://dx.doi.org/10.4310/hha.2009.v11.n2.a9.

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Jarboui, Noômen, Naseam Al-Kuleab, and Omar Almallah. "Ring Extensions with Finitely Many Non-Artinian Intermediate Rings." Journal of Mathematics 2020 (November 12, 2020): 1–6. http://dx.doi.org/10.1155/2020/7416893.

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The commutative ring extensions with exactly two non-Artinian intermediate rings are characterized. An initial step involves the description of the commutative ring extensions with only one non-Artinian intermediate ring.
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Hijriati, Na'imah, Sri Wahyuni, and Indah Emilia Wijayanti. "Generalization of Schur's Lemma in Ring Representations on Modules over a Commutative Ring." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 751–61. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3285.

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Let $ R, S $ be rings with unity, $ M $ a module over $ S $, where $ S $ a commutative ring, and $ f \colon R \rightarrow S $ a ring homomorphism. A ring representation of $ R $ on $ M $ via $ f $ is a ring homomorphism $ \mu \colon R \rightarrow End_S(M) $, where $ End_S(M) $ is a ring of all $ S $-module homomorphisms on $ M $. One of the important properties in representation of rings is the Schur's Lemma. The main result of this paper is partly the generalization of Schur's Lemma in representations of rings on modules over a commutative ring
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Dissertations / Theses on the topic "Commutative ring"

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Duncan, A. J. "Two topics in commutative ring theory." Thesis, University of Edinburgh, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234124.

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Hedenlund, Alice. "Galois Theory of Commutative Ring Spectra." Thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183512.

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This thesis discusses Galois theory of ring spectra in the sense of John Rognes. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce ring spectra using the symmetric spectra of Hovey, Shipley and Smith, and discuss the symmetric monoidal model structure on this category. We define and give results for Galois extensions of these objects. We also give examples involving Eilenberg-Mac Lane spectra of commutative rings, topological K-theory spectra and cochain algebras of these. Galois extensions of ring spectra are compared to Ga-lois extensions of commutative rings especially relating to faithfulness, a property that is implicit in the latter, but not in the former. This is proven by looking at extensions of cochain algebras using Eilenberg-Mac Lane spectra. We end by contrasting this to cochain algebra extensions using K-theory spectra, and show that such extensions are not Galois, using methods of Baker and Richter.
Denna uppsats behandlar Galoisutvidgningar av ringspektra som först introducerade av Rognes. Målet är att ge en klar introduktion för en sta-bil grund för vidare studier inom ämnet. Vi introducerar ringspektra genom att använda oss av symmetris-ka spektra utvecklade av Hovey, Shipley och Smith, och diskuterar den symmetriskt monoidiala modelstrukturen på denna kategori. Vi definierar och ger resultat för Galoisutvidgningar av dessa objekt. Vi ger också en mängd exempel, som till exempel utvidgningar av Eilenberg-Mac Lane spektra av kommutativa ringar, topologiska K-teorispektra och koked-jealgebror. Galoisutvidgningar av ringspektra jämförs med Galoisutvidgningar av kommutativa ringar, speciellt med avseende pa˚ trogenhet, en egenskap som ¨ar en inneboende egenskap hos den senare men inte i den förra. Detta visas genom att betrakta utvidgningar av kokedjealgebror av Eilenberg-Mac Lane spektra. Vi avslutar med att jämföra detta med kokedjealgebrautvidgningar av K-teorispektra och visar att sådana inte är Galois genom att använda metoder utvecklade av Baker och Richter
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Hasse, Erik Gregory. "Lowest terms in commutative rings." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6433.

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Putting fractions in lowest terms is a common problem for basic algebra courses, but it is rarely discussed in abstract algebra. In a 1990 paper, D.D. Anderson, D.F. Anderson, and M. Zafrullah published a paper called Factorization in Integral Domains, which summarized the results concerning different factorization properties in domains. In it, they defined an LT domain as one where every fraction is equal to a fraction in lowest terms. That is, for any x/y in the field of fractions of D, there is some a/b with x/y=a/b and the greatest common divisor of a and b is 1. In addition, R. Gilmer included a brief exercise concerning lowest terms over a domain in his book Multiplicative Ideal Theory. In this thesis, we expand upon those definitions. First, in Chapter 2 we make a distinction between putting a fraction in lowest terms and reducing it to lowest terms. In the first case, we simply require the existence of an equal fraction which is in lowest terms, while the second requires an element which divides both the numerator and the denominator to reach lowest terms. We also define essentially unique lowest terms, which requires a fraction to have only one lowest terms representation up to unit multiples. We prove that a reduced lowest terms domain is equivalent to a weak GCD domain, and that a domain which is both a reduced lowest terms domain and a unique lowest terms domain is equivalent to a GCD domain. We also provide an example showing that not every domain is a lowest terms domain as well as an example showing that putting a fraction in lowest terms is a strictly weaker condition than reducing it to lowest terms. Next, in Chapter 3 we discuss how lowest terms in a domain interacts with the polynomial ring. We prove that if D[T] is a unique lowest terms domain, then D must be a GCD domain. We also provide an alternative approach to some of the earlier results using the group of divisibility. So far, all fractions have been representatives of the field of fractions of a domain. However, in Chapter 4 we examine fractions in other localizations of a domain. We define a necessary and sufficient condition on the multiplicatively closed set, and then examine how this relates to existing properties of multiplicatively closed sets. Finally, in Chapter 5 we briefly examine lowest terms in rings with zero divisors. Because many properties of GCDs do not hold in such rings, this proved difficult. However, we were able to prove some results from Chapter 2 in this more general case.
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Stalvey, Harrison. "Weak Primary Decomposition of Modules Over a Commutative Ring." Digital Archive @ GSU, 2010. http://digitalarchive.gsu.edu/math_theses/84.

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This paper presents the theory of weak primary decomposition of modules over a commutative ring. A generalization of the classic well-known theory of primary decomposition, weak primary decomposition is a consequence of the notions of weakly associated prime ideals and nearly nilpotent elements, which were introduced by N. Bourbaki. We begin by discussing basic facts about classic primary decomposition. Then we prove the results on weak primary decomposition, which are parallel to the classic case. Lastly, we define and generalize the Compatibility property of primary decomposition.
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Alshaniafi, Y. S. "The homological grade of a module over a commutative ring." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280830.

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Baig, Muslim. "Primary Decomposition and Secondary Representation of Modules over a Commutative Ring." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/69.

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This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particular, the existence of a secondary representation for Artinian modules. It concludes with some interesting examples of both secondary and representable modules, highlighting the consequences of the results thus established.
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Philippoussis, Anthony. "Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly [pi]-regular ring." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/MQ39934.pdf.

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Edmonds, Ranthony A. C. "Factorization in polynomial rings with zero divisors." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/3248.

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Factorization theory is concerned with the decomposition of mathematical objects. Such an object could be a polynomial, a number in the set of integers, or more generally an element in a ring. A classic example of a ring is the set of integers. If we take any two integers, for example 2 and 3, we know that $2 \cdot 3=3\cdot 2$, which shows that multiplication is commutative. Thus, the integers are a commutative ring. Also, if we take any two integers, call them $a$ and $b$, and their product $a\cdot b=0$, we know that $a$ or $b$ must be $0$. Any ring that possesses this property is called an integral domain. If there exist two nonzero elements, however, whose product is zero we call such elements zero divisors. This thesis focuses on factorization in commutative rings with zero divisors. In this work we extend the theory of factorization in commutative rings to polynomial rings with zero divisors. For a commutative ring $R$ with identity and its polynomial extension $R[X]$ the following questions are considered: if one of these rings has a certain factorization property, does the other? If not, what conditions must be in place for the answer to be yes? If there are no suitable conditions, are there counterexamples that demonstrate a polynomial ring can possess one factorization property and not another? Examples are given with respect to the properties of atomicity and ACCP. The central result is a comprehensive characterization of when $R[X]$ is a unique factorization ring.
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Oyinsan, Sola. "Primary decomposition of ideals in a ring." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3289.

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The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.
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Nossem, Nicole. "On the perfect closure of a commutative Noetherian ring of positive prime characteristic." Thesis, University of Sheffield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251466.

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Books on the topic "Commutative ring"

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Commutative ring theory. Cambridge [Cambridgeshire]: Cambridge University Press, 1986.

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Jain, Surender Kumar, and Sergio R. López-Permouth, eds. Non-Commutative Ring Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0091244.

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Lee, John. Commutative rings: New research. New York: Nova Science Publishers, 2009.

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Chapman, Scott T. Non-Noetherian Commutative Ring Theory. Boston, MA: Springer US, 2000.

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Chapman, Scott T., and Sarah Glaz, eds. Non-Noetherian Commutative Ring Theory. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3180-4.

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Greither, Cornelius. Cyclic Galois extensions of commutative rings. Berlin: Springer-Verlag, 1992.

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International Conference on Commutative Ring Theory (3rd Fès, Morocco). Advances in commutative ring theory: Proceedings of the Third International Conference on Commutative Ring Theory in Fez, Morocco. New York: Marcel Dekker, 1999.

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Tennessee-Knoxville), John H. Barrett Memorial Lectures and Conference on Commutative Ring Theory (1994 University of. Zero-dimensional commutative rings: Proceedings of the 1994 John H. Barrett Memorial Lectures and Conference on Commutative Ring Theory. New York: M. Dekker, 1995.

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1947-, Fontana Marco, Kabbaj Salah-Eddine 1959-, and Wiegand Sylvia, eds. Commutative ring theory and applications: Proceedings of the fourth international conference. New York: Marcel Dekker, 2003.

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Karpilovsky, Gregory. Unit groups of group rings. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Book chapters on the topic "Commutative ring"

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Smith, S. P. "Differential operators on commutative algebras." In Ring Theory, 165–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076323.

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Cahen, Paul-Jean, Marco Fontana, Sophie Frisch, and Sarah Glaz. "Open Problems in Commutative Ring Theory." In Commutative Algebra, 353–75. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0925-4_20.

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Goldie, A. W. "Non-Commutative Localisation." In Some Aspects of Ring Theory, 241–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11036-8_7.

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Susperregui, Julian. "On determinantal ideals over certain non commutative rings." In Ring Theory, 269–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0100932.

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Dougherty, Steven T. "Ring Theory." In Algebraic Coding Theory Over Finite Commutative Rings, 13–28. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59806-2_2.

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Gilmer, Robert. "Commutative Rings of Dimension 0." In Non-Noetherian Commutative Ring Theory, 229–49. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3180-4_10.

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Badawi, Ayman. "On the Total Graph of a Ring and Its Related Graphs: A Survey." In Commutative Algebra, 39–54. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0925-4_3.

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Zafrullah, Muhammad. "Putting T-Invertibility to Use." In Non-Noetherian Commutative Ring Theory, 429–57. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3180-4_20.

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Chapman, Scott T., and Sarah Glaz. "One Hundred Problems in Commutative Ring Theory." In Non-Noetherian Commutative Ring Theory, 459–76. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3180-4_21.

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Anderson, D. D. "GCD Domains, Gauss’ Lemma, and Contents of Polynomials." In Non-Noetherian Commutative Ring Theory, 1–31. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3180-4_1.

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Conference papers on the topic "Commutative ring"

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Ghowsi, Hossein. "Situation of commutative for near ring." In The First Regional Conference on the Advanced Mathematics and Its Applications. Ispacs GmbH, 2012. http://dx.doi.org/10.5899/2012/cjac-001-009.

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Tang, Gaohua, Huadong Su, and Yangjiang Wei. "Commutative rings and zero-divisor semigroups of regular polyhedrons." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0017.

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Akbiyik, Seda, and Bayram Ali Ersoy. "Cyclic codes over a non-commutative ring." In 2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). IEEE, 2017. http://dx.doi.org/10.1109/icmsao.2017.7934873.

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Abbasi, A. "On the T-graph of a Commutative Ring." In 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012). IEEE, 2012. http://dx.doi.org/10.1109/asonam.2012.235.

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Rilwan, N. Mohamed, and R. Radha. "Decycling on zero divisor graphs of commutative ring." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0016962.

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Yoshino, Yuji. "Introduction to Auslander-Bridger theory for unbounded projective complexes over commutative Noetherian rings." In The Eighth China–Japan–Korea International Symposium on Ring Theory. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811230295_0005.

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Bashkirov, Evgenii L., and Hasan Eser. "On linear groups of degree 2 over a finite commutative ring." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893832.

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Jamsheena, P., and A. V. Chithra. "On the domination of the essential ideal graph of a commutative ring." In INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0046232.

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Cheng, Harry H., and Sean Thompson. "Dual Polynomials and Complex Dual Numbers for Analysis of Spatial Mechanisms." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1221.

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Abstract Complex dual numbers w̌1=x1+iy1+εu1+iεv1 which form a commutative ring are for the first time introduced in this paper. Arithmetic operations and functions of complex dual numbers are defined. Complex dual numbers are used to solve dual polynomial equations. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of special configurations of the RCCC spatial mechanism. Numerical solutions for dual polynomial equations and complex dual numbers are conveniently implemented in the CH language environment for analysis of the RCCC spatial mechanism. Like the dual number, the complex dual number is a useful mathematical tool for analytical and numerical treatment of spatial mechanisms.
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KLINGLER, LEE, and LAWRENCE S. LEVY. "REPRESENTATION TYPE OF COMMUTATIVE NOETHERIAN RINGS (INTRODUCTION)." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0010.

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Reports on the topic "Commutative ring"

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Yıldız, Eda, Ünsal Tekir, and Suat Koç. (2,J)-Ideals in Commutative Rings. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, September 2020. http://dx.doi.org/10.7546/crabs.2020.09.02.

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