Results 101 to 110 of about 335,227 (157)
On the Multiplicative Semigroup of a Commutative Ring [PDF]
Proceedings of the American Mathematical Society, 1959 This note establishes the theorem that a commutative ring is finite provided its multiplicative semigroup is finitely generated. The author does not know whether the assumption of commutativity is necessary for the truth of the theorem.
openaire +1 more source
Transfinite idealization and commutative rings of triangular matrices
, 2009 The self-idealization of a commutative ring is iterated countably many times, producing an inverse-direct system of rings.
SALCE, LUIGI
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A commutative version of the group ring
We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings.
Mannan, W.H.
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A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
Open Mathematics, 2015 Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable ...
Zhao Xiangui, Zhang Yang
doaj +1 more source
Finitely embedded commutative rings
, 1991 A theorem of Ginn and Moss [G-M] states that a right finitely embedded (= with finite essential right socle) two-sided Noetherian ring is Artinian. An example of Schelter and Small [S-S] can be applied to show that the theorem fails for right finitely ...
Carl Faith
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Envelopes of commutative rings
, 2009 Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an F-envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains.
Saorín Castaño, Manuel, Parra, Rafael
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Commutative Rings Behind Divisible Residuated Lattices
MathematicsDivisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek’s basic logic with an important significance in the study of fuzzy logic.
Cristina Flaut, Dana Piciu
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs
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
doaj +1 more source
Directed Graphs of Commutative Rings [PDF]
, 2017 The directed graph of a commutative ring is a graph representation of its additive and multiplicative structure. Using the mapping (a,b) → (a+b,a ⋅ b) one can create a directed graph for every finite, commutative ring.
Skinner, Jared, Hausken, Seth
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, 2014 A commutative ring R is called an AM-ring (for allgemeine Multiplikationsring) if whenever A and B are ideals of R with A < B (i.e., A properly contained in B) then there exists an ideal C such that A = BC.
P. F. Smith
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