Results 11 to 20 of about 327,963 (245)
A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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An Introduction to i-Commutative Rings
MathematicsIn this paper, we introduce a new class of rings, called i-commutative rings, by extending the concept of commutative-like rings using idempotent elements.
Muhammad Saad +3 more
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Poincaré duality in Hochschild (co)homology [PDF]
, 2006 These are notes on van den Bergh’s analogue of Poincar´e duality in Hochschild (co)homology [VdB98]. They are based on survey talks that I gave in 2006 in G¨ottingen, Cambridge and Warsaw and consist of an elementary explanation of the proof in terms ...
Kraehmer, U.
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources
NeutroAlgebra of Idempotents in Group Rings [PDF]
Neutrosophic Sets and Systems, 2022 In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1.
Vasantha Kandasamy +1 more
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On the Genus of the Idempotent Graph of a Finite Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2021 Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0.
Belsi G. Gold, Kavitha S., Selvakumar K.
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Expansivity on commutative rings [PDF]
Topology and its Applications, 2020 In this article we extend the notion of expansivity from topological dynamics to automorphisms of commutative rings with identity. We show that a ring admits a 0-expansive automorphism if and only if it is a finite product of local rings. Generalizing a well known result of compact metric spaces, we prove that if a ring admits a positively expansive ...
Alfonso Artigue, Mariana Haim
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Reticulation of Quasi-commutative Algebras [PDF]
Journal of Mahani Mathematical Research, 2023 The commutator theory, developed by Fresee and McKenzie in the framework of a congruence-modular variety $\mathcal{V}$, allows us to define the prime congruences of any algebra $A\in \mathcal{V}$ and the prime spectrum $Spec(A)$ of $A$.
G. Georgescu
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Centrally Prime Rings which are Commutative [PDF]
Kirkuk Journal of Science, 2006 In this paper the definition of centrally prime rings is introduced , our main purpose is to classify those centrally prime rings which are commutative and so that several conditions are given each of which makes a centrally prime ring commutative.
Adil K.Jabbar
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, 2021 By studying and using the quasi-pure part concept, we improve some statements and show that some assumptions in some articlesare superfluous. We give some characterizations of Gelfand rings. For example: we prove that R is Gelfand if and only if m(∑ α∈A Iα) =∑α∈A m(Iα), for each family {Iα}α∈A of ideals of R, in addition if R is semiprimitive and Max(R)
Badie, Mehdi +2 more
openaire +3 more sources