Results 31 to 40 of about 97,313 (257)
The Ideal Intersection Property for Groupoid Graded Rings [PDF]
, 2010 We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring ...
Caenepeel S. +25 more
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Commutativity and structure of rings with commuting nilpotents [PDF]
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 < x> such that x − x2x′ϵN, where <x> denotes the subring generated by x, (iii) for every x, y in R, there exists an integer n = n(x, y) ≥ 1 such that both (xy) n − (yx ...
Hazar Abu-Khuzam, Adil Yaqub
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Pure Graph of a Commutative Ring
Wasit Journal for Pure Sciences, 2023 A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????
Nermen J.Khalel +2 more
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Polynomial Rings over Pseudovaluation Rings
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be a ring. Let σ be an automorphism of R. We define a σ-divided ring and prove the following. (1) Let R be a commutative pseudovaluation ring such that x∉P for any P∈Spec(R[x,σ]) . Then R[x,σ] is also a pseudovaluation ring.
V. K. Bhat
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Classifying birationally commutative projective surfaces [PDF]
, 2009 Let R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3 over an uncountable algebraically closed field. Suppose that the graded quotient ring of R is a skew-Laurent ring over a field; we say that R is a birationally commutative ...
Sierra, Susan J.
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Characterization of fuzzy neighborhood commutative division rings II
International Journal of Mathematics and Mathematical Sciences, 1995 In [4] we produced a characterization of fuzzy neighborhood commutative division rings; here we present another characterization of it in a sense that we minimize the conditions so that a fuzzy neighborhood system is compatible with the commutative ...
T. M. G. Ahsanullah, Fawzi A. Al-Thukair
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Valuations on a Commutative Ring [PDF]
Proceedings of the American Mathematical Society, 1969 By a valuation on a commutative ring R, we mean a pair (v, I), where r is an ordered (mult) group with a zero adjoined and v is a map of R onto r satisfying (1) v(xy) =v(x)v(y) for all x, yER, (2) v(x+y)?
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On commutators and derivations in rings
Journal of Algebra, 2004 AbstractWe consider the problem when the product of certain higher commutators arising from a fixed element in a ring lies in the ideal generated by some power of this element. The result which we obtain is applied to the study of (generalized) derivations in rings and (Banach) algebras.
Matej Brešar +2 more
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Generalized periodic and generalized Boolean rings
International Journal of Mathematics and Mathematical Sciences, 2001 We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply
Howard E. Bell, Adil Yaqub
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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 ( a 1 , a 2 ) ∈ R × R ({a_1},{a_2}) \in R \times R there exists a pair (
openaire +2 more sources