Results 11 to 20 of about 1,268,119 (187)
Commutativity theorems for rings and groups with constraints on commutators [PDF]
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. If n‐torsion freeness of R is replaced by “m, n are relatively prime,” then R is still commutative.
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, 2021 In these notes, we introduce the reader to the categorical commutator theory (of subobjects), following the formal approach given by Mantovani and Metere in 2010.
A. Montoli +3 more
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A Geometric Study of Commutator Subgroups [PDF]
, 2009 Let G be a group and G' its commutator subgroup. Commutator length (cl) and stable commutator length (scl) are naturally defined concepts for elements of G'. We study cl and scl for two classes of groups.
Zhuang, Dongping, Dongping Zhuang
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COMMUTATIVITY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS
Tamkang Journal of Mathematics, 1995 Let $R$ be a left (resp. right) $s$-unital ring and $m$ be a positive integer. Suppose that for each $y$ in $R$ there exist $J(t)$, $g(t)$, $h(t)$ in $Z[t]$ such that $x^m[x,y]= g(y)[x,y^2f(y)]h(y)$ (resp. $[x,y]x^m= g(y)[x,y^2f(y)]h(y))$ for all $x$ in $R$. Then $R$ is commutative (and conversely).
Abujabal, H. A. S., Ashraf, Mohd.
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Associative-Commutative Deducibility Constraints [PDF]
, 2007 We consider deducibility constraints, which are equivalent to particular Diophantine systems, arising in the automatic verification of security protocols, in presence of associative and commutative symbols. We show that deciding such Diophantine systems is, in general, undecidable. Then, we consider a simple subclass, which we show decidable.
Sergiu Bursuc +2 more
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On commutativity of rings with constraints on subsets [PDF]
Czechoslovak Mathematical Journal, 1993 Summary: Let \(R\) be a ring with center \(Z(R)\), and let \(A(R)\) be an appropriate subset of \(R\). In this paper, it is shown that \(R\) is commutative if and only if for every \(x,y\in R\), there exist integers \(k=k(x,y)\geq 1\), \(m=m(x,y)>1\), and \(n=n(x,y)\geq 1\) such that \([x,x^ny-y^mx^k]=0\) and for each \(x\in R\) either \(x\in Z(R ...
Abujabal, H. A. S. +3 more
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Hypercyclicity Properties of Commutator Maps [PDF]
, 2017 We investigate the hypercyclic properties of commutator operators acting on separable Banach ideals of operators. As the main result we prove the commutator map induced by scalar multiples of the backward shift operator fails to be hypercyclic on the ...
Tylli, Hans-Olav +2 more
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Commutative idempotent groupoids and the constraint satisfaction problem
Algebra universalis, 2015 A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak near-unanimity term, then the corresponding constraint satisfaction problem is tractable. A binary operation is weak near-unanimity if and only if it is both commutative and idempotent. Thus if the dichotomy conjecture
Bergman, Clifford, Failing, David
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The role of commutativity in constraint propagation algorithms [PDF]
ACM Transactions on Programming Languages and Systems, 2000 Constraing propagation algorithms form an important part of most of the constraint programming systems. We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In this framework we proceed in two steps.
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Commutativity results for rings with certain constraints on commutators
Proyecciones (Antofagasta), 2018 We investigate here the commutativity of a left (resp. right) s-unital ring R satisfying the polynomial identity yr [xny] xt = ±y3 [x, ym] (resp. yr [xn, y] xt = ± [x, ym] ys ) for some non-negative integers m >0, n > 0, r, s and t such that n + t > 1 (resp. m + s > 1 for r = 0). For such a ring R, we prove the commutativity if n + t > 1,
Hamza A. S. Abujabal, Veselin Peric
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