Results 31 to 40 of about 6,335 (253)
On commutators and derivations in rings
Journal of Algebra, 2004 Let \(a\) be a fixed element of the ring \(R\); and for each \(x_0\in R\), define higher commutators \(x_1,x_2,\dots\) inductively by \(x_i=[a,x_{i-1}]\). The authors' main purpose is to study when products \(b_ic_j\) or integer multiples of such products lie in the ideal generated by some power of \(a\).
Brešar, Matej +2 more
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Irish Mathematical Society Bulletin, 1996 Summary: We exhibit with proof a ring of minimal order in which the commutator subset is not a subring.
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A Commutativity Theorem for Rings [PDF]
Proceedings of the American Mathematical Society, 1976 Let R R be any associative ring. Suppose that for every pair
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, 2002 The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all ...
Vasantha, Kandasamy
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Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases [PDF]
, 2010 We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras.
Regensburger, Georg +4 more
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Commutativity theorems for rings and groups with constraints on commutators
International Journal of Mathematics and Mathematical Sciences, 1984 Let n>1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn,y]=[x,ym]ys for all x, y in R. If, further, R is n-torsion free, then R is commutativite.
Evagelos Psomopoulos
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Commutativity and structure of rings with commuting nilpotents
International Journal of Mathematics and Mathematical Sciences, 1983 Let R be a ring and let N denote the set of nilpotent elements of R. Let Z denote the center of R. Suppose that (i) N is commutative, (ii) for every x in R there exists x′ϵ such that x−x2x′ϵN, where denotes the subring generated by x, (iii) for every x ...
Hazar Abu-Khuzam, Adil Yaqub
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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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An iteration technique and commutativity of rings
International Journal of Mathematics and Mathematical Sciences, 1990 Through much shorter proofs, some new commutativity theorems for rings with unity have been obtained. These results either extend or generalize a few well-known theorems. Our method of proof is based on an iteration technique.
H. A. S. Abujabal, M. S. Khan
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Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsAn recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
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