Results 11 to 20 of about 97,313 (257)
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.
M. F. Smiley
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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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Enumeration of Neutrosophic Involutions over Finite Commutative Neutrosophic Rings [PDF]
Neutrosophic Sets and Systems, 2023 A finite commutative ring involution is the multiplicative inverse of the element attribute R is the element itself. This classical characteristic of a finite commutative ring makes Neutrosophic involutions possible, which are counted, listed and ...
T. Chalapathi +2 more
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Commutative endomorphism rings [PDF]
Pacific Journal of Mathematics, 1973 Samuel H. Cox
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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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AIMS Mathematics, 2022 An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which ...
Yousef Alkhamees, Sami Alabiad
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Ratio Mathematica, 2023 We deliberate a substructure of a near ring called mediality so as to create a new platform, on which many of the properties like commutativity, regular, idempotent and zero symmetric are applied with.
Dhivya C, Radha D
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ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS [PDF]
Journal of Algebraic Systems, 2019 Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$
M. Rezagholibeigi, A. R. Naghipour
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Generalized Commutative Rings [PDF]
Nagoya Mathematical Journal, 1966 Among his various interests in algebra Nakayama also took part in the various researches, published in the early and middle 1950’s, which dealt with the commutativity of rings. This paper, which studies a problem of a related sort, thus seems appropriate in a Journal honoring his memory.We shall study a certain class of rings which satisfy a weak form ...
Belluce, L. P. +2 more
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Benefits of Open Quantum Systems for Quantum Machine Learning
Advanced Quantum Technologies, EarlyView., 2023 Quantum machine learning (QML), poised to transform data processing, faces challenges from environmental noise and dissipation. While traditional efforts seek to combat these hindrances, this perspective proposes harnessing them for potential advantages. Surprisingly, under certain conditions, noise and dissipation can benefit QML.
María Laura Olivera‐Atencio +2 more
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