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Relevant bibliographies by topics / Commutative ring

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Academic literature on the topic 'Commutative ring'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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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 (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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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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Reddy Y., Madana Mohana. "Some Studies on Commutative Rings in Commutative Algebra." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 1221–26. http://dx.doi.org/10.52783/tjjpt.v44.i4.1002.

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In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of noncommutative ring where multiplication is not required to be commutative.

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Lawson, Tyler. "Commutative Γ-rings do not model all commutative ring spectra". Homology, Homotopy and Applications 11, № 2 (2009): 189–94. http://dx.doi.org/10.4310/hha.2009.v11.n2.a9.

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Dobbs, David. "On minimal ring extensions of finite rings." Gulf Journal of Mathematics 12, no. 2 (2022): 1–30. http://dx.doi.org/10.56947/gjom.v12i2.677.

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Two conditions, (i) and (ii), are defined, that may hold for a given (unital) ring extension R ⊂ S of (unital, associative, not necessarily commutative) finite rings. It is shown that if S is commutative, then ``"either (i) or (ii)” is a necessary and sufficient condition for R ⊂ S to be a minimal ring extension; and that for such extensions, (i) and (ii) are logically independent. For extensions with S (finite and) noncommutative, "either (i) or (ii)” is neither necessary nor sufficient for R ⊂ S to be a minimal ring extension; and for such minimal ring extensions, (i) and (ii) are logically

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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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Bataineh, Malik, Mashhoor Refai, Rashid Abu-Dawwas, and Khaldoun Al-Zoubi. "Semi-commutativity of graded rings and graded modules." Proyecciones (Antofagasta) 41, no. 6 (2022): 1377–95. http://dx.doi.org/10.22199/issn.0717-6279-4951.

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A ring R is said to be semi-commutative if whenever a, b ∈ R such that ab = 0, then aRb = 0. In this article, we introduce the concepts of g−semi-commutative rings and g−N−semi-commutative rings and we introduce several results concerning these two concepts. Let R be a G-graded ring and g ∈ supp(R, G). Then R is said to be a g−semi-commutative if whenever a, b ∈ R with ab = 0, then aRgb = 0. Also, R is said to be a g − N−semi-commutative if for any a ∈ R and b ∈ N(R) ⋂ Ann(a), bRg ⊆ Ann(a). We introduce an example of a G-graded ring R which is g − N-semi-commutative for some g ∈ supp(R, G) but

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Akgunes, Nihat, and Yasar Nacaroglu. "Some properties of zero divisor graph obtained by the ring Zp × Zq × Zr." Asian-European Journal of Mathematics 12, no. 06 (2019): 2040001. http://dx.doi.org/10.1142/s179355712040001x.

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The concept of zero-divisor graph of a commutative ring was introduced by Beck [Coloring of commutating ring, J. Algebra 116 (1988) 208–226]. In this paper, we present some properties of zero divisor graphs obtained from ring [Formula: see text], where [Formula: see text] and [Formula: see text] are primes. Also, we give some degree-based topological indices of this special graph.

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Udjiani, Titi, Suryoto Suryoto, and Harjito Harjito. "NORMAL ELEMENT ON IDENTIFY PROPERTIES." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 2 (2018): 95. http://dx.doi.org/10.14710/jfma.v1i2.16.

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Abstract. One type of element in the ring with involution is normal element. Their main properties is commutative with their image by involution in ring. Group invers of element in ring is always commutative with element which is commutative with itself. In this paper, properties of normal element in ring with involution which also have generalized Moore Penrose invers are constructed by using commutative property of group invers in ring. Keywords: Normal, Moore Penrose, group, involution

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Zabavsky, B. V., O. Romaniv, B. Kuznitska, and T. Hlova. "Comaximal factorization in a commutative Bezout ring." Algebra and Discrete Mathematics 30, no. 1 (2020): 150–60. http://dx.doi.org/10.12958/adm1203.

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Dissertations / Theses on the topic "Commutative ring"

1

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

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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 inc

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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 particula

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Martini, Lorenzo. "Local coherence of hearts in the derived category of a commutative ring." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/354322.

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Approximation theory is a fundamental tool in order to study the representation theory of a ring R. Roughly speaking, it consists in determining suitable additive or abelian subcategories of the whole module category Mod-R with nice enough functorial properties. For example, torsion theory is a well suited incarnation of approximation theory. Of course, such an idea has been generalised to the additive setting itself, so that both Mod-R and other interesting categories related with R may be linked functorially. By the seminal work of Beilinson, Bernstein and Deligne (1982), the derived categor

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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 i

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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 d

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Books on the topic "Commutative ring"

1

Houston, Evan, Paul-Jean Cahen, Marco Fontana, and Salah-Eddine Kabbaj. Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924.

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Fontana, Marco, Paul-Jean Cahen, Douglas L. Costa, and Sarah-Eddine Kabbaj. Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421917.

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

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

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

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T, Chapman Scott, and Glaz Sarah 1947-, eds. Non-Noetherian commutative ring theory. Kluwer Academic Publishers, 2000.

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

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Dobbs, David. Advances in Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003419815.

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

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10

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. Marcel Dekker, 1999.

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Book chapters on the topic "Commutative ring"

1

Anderson, David F., and Carla Scherpenisse. "Factorization in K[S]." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-5.

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Tartarone, Francesca. "On the Krull Dimension of Int(D) When D Is a Pullback." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-41.

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Khalis, Mohammed, and Driss Nour El Abidine. "On the Class Group of a Pullback." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-36.

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Bouacida, Ezzeddine, Othman Echi, and Ezzeddine Salhi. "Nonfinite Heights." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-12.

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Cahen, Paul-Jean, and Thomas G. Lucas. "The Special Trace Property." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-16.

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Kaidi, Amin, Dolores Martin Barquero, and Candido Martin Gonzalez. "On the Socle-Fine Notion and Modules of Finite Length." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-35.

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Chabert, J. L. "Skolem Properties for Several Indeterminates." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-18.

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Bouchiba, Samir, Florida Girolami, and Salah-Eddine Kabbaj. "The Dimension of Tensor Products of AF-Rings." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-14.

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Dichi, Henri. "Filtrations, Prüferian Closure Relative to a Module." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-22.

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Facchini, Alberto, and Carl Faith. "FP-Injective Quotient Rings and Elementary Divisor Rings." In Commutative Ring Theory. CRC Press, 2023. http://dx.doi.org/10.1201/9781003421924-27.

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Conference papers on the topic "Commutative ring"

1

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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Nawaf, Alaa J., Nabeel E. Arif, and Ali A. Aubad. "Non-zero graph of a commutative ring Zp." In 3RD INTERNATIONAL CONFERENCE ON MATHEMATICS, AI, INFORMATION AND COMMUNICATION TECHNOLOGIES: ICMAICT2023. AIP Publishing, 2025. https://doi.org/10.1063/5.0258852.

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Hidayati, Nur Aini, Mohammad Agung, and Indriati Nurul Hidayah. "Sufficient condition of symmetric biderivation on prime ring to be commutative ring." In PROCEEDINGS OF THE II INTERNATIONAL SCIENTIFIC CONFERENCE ON ADVANCES IN SCIENCE, ENGINEERING AND DIGITAL EDUCATION: (ASEDU-II 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0110466.

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Authman, Mohammed N., Nazar H. Shuker, and Husam Q. Mohammad. "Some properties of idempotent divisor graph of commutative ring." In 1ST SAMARRA INTERNATIONAL CONFERENCE FOR PURE AND APPLIED SCIENCES (SICPS2021): SICPS2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0120915.

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Kurniawan, Vika Yugi, Bayu Purboutomo, and Santoso Budi Wiyono. "Algorithm for constructing triple unit graph of commutative ring." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICS: EDUCATION, THEORY & APPLICATION (ICMETA) 2022. AIP Publishing, 2025. https://doi.org/10.1063/5.0261929.

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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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Reports on the topic "Commutative ring"

1

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

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