Results 61 to 70 of about 335,227 (157)
Stability in Commutative Rings
TURKISH JOURNAL OF MATHEMATICS, 2020 Summary: Let \(R\) be a commutative ring with zero-divisors and \(I\) an ideal of \(R\). \(I\) is said to be ES-stable if \(JI = I^2\) for some invertible ideal \(J\subseteq I\), and \(I\) is said to be a weakly ES-stable ideal if there is an invertible fractional ideal \(J\) and an idempotent fractional ideal \(E\) of \(R\) such that \(I = JE\).
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Closure operations in commutative rings [PDF]
, 2012 The purpose of this study is to survey different types of closures and closure operations on commutative rings and ...
Samsam, Chloette Joy
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Some Examples of BL-Algebras Using Commutative Rings
Mathematics, 2022 BL-algebras are algebraic structures corresponding to Hajek’s basic fuzzy logic. The aim of this paper is to analyze the structure of BL-algebras using commutative rings. Due to computational considerations, we are interested in the finite case.
Cristina Flaut, Dana Piciu
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Non-commutative reduction rings [PDF]
, 1999 Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Gröbner bases can be characterized by properties of reduction relations associated ...
Birgit Reinert +3 more
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Non-commutative Henselian rings
, 2009 Non-commutative Henselian rings are defined and some basic properties of them are discussed. It is shown that a local ring which is complete in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.
Aryapoor, Masood,, Masood Aryapoor
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Subrings of I-rings and S-rings
International Journal of Mathematics and Mathematical Sciences, 1997 Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
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Ring Extensions with Finitely Many Non-Artinian Intermediate Rings
Journal of Mathematics, 2020 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.
Noômen Jarboui +2 more
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Quasi-Regular Graphs Associated with Commutative Rings
Journal of Mathematics, 2022 One of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented.
Nasr Zeyada +2 more
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Acyclic Complexes and Graded Algebras
Mathematics, 2023 We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated ...
Chaoyuan Zhou
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Remarks on the commutativity of rings [PDF]
Proceedings of the American Mathematical Society, 1959 Introduction. A celebrated theorem of N. Jacobson [7] asserts that if (1) Xn(z) =x for every x in a ring R, where n(x) is an integer greater than one, then R is commutative. In a recent paper [2], I. N. Herstein has shown that it is enough to require that (1) holds for those x in R which are commutators: x= [y, z] =yz-zy of two elements of R.
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