Results 131 to 140 of about 335,227 (157)

On the Commutativity of a Ring with Identity

Canadian Mathematical Bulletin, 1984
AbstractLet R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R:(I)xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0;(II)xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0;(III)xmyn = ynxm and m! n! x≠0 except x = 0;(IV)(xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite ...
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A Condition for the Commutativity of Rings

Canadian Journal of Mathematics, 1957
A well-known theorem of Jacobson (1) asserts that if every element a of a ring A satisfies a relation an(a) = a where n(a) > 1 is an integer, then A is a commutative ring.
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Commutativity of rings with constraints on commutators

2000
This paper studies commutativity of rings \(R\) satisfying polynomial identities of the form\break \(x^t[x^n,y]y^r=[x,y^m]y^s\) and three similar forms, where \(n,m,r,s,t\) are suitably-chosen nonnegative integers. Whether the theorems are correct as stated is not clear, but for some \((n,m,r,s,t)\) the proofs given do not work.
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Commutativity of rings with constraints on commutators

Results in Mathematics, 1985
Let F denote a commutative ring, \(F\) the corresponding ring of polynomials in two non-commuting indeterminates, and F[X,Y] the ring of polynomials in two commuting indeterminates. A polynomial \(f(X,Y)\in F\) is called admissible if each of its monomials has length at least 3 and f(X,Y) has trivial image under the natural F-algebra map from \(F\) to ...
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On the Commutativity of Rings with Constraints on Commutators.

International Journal of Mathematics and Computer Science
We investigate the commutativity of rings with identity satisfying identities involving commutators and their powers in the class of M!-torsion-free rings. We obtain sufficient conditions for commutativity from identities of the forms [x,y^m]=0, [x^n,y^m]=0, and [x^n,y]=[x,y^m], as well as from conditions on mappings preserving commutators.
Utsanee Leerawat, Chitlada Somsup
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Commutative Rings

Lecture Notes in Mathematics, 1973
Irving Kaplansky
exaly  

The Total Graph of a Commutative Ring

Journal of Algebra, 2008
Ayman Badawi, David F Anderson
exaly  

Commutative Coherent Rings

Lecture Notes in Mathematics, 1989
Sarah Glaz
exaly  

Commutative rings III

2010
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Analysis of Nonlinear Time-Delay Systems Using Modules Over Non-Commutative Rings

Automatica, 2002
Xiaohua Xia, Claude Moog, Petr Zagalak
exaly