Commutativity theorems for rings and groups with constraints on commutators

Evagelos Psomopoulos

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-5

Abstract:

Let n > 1 , m , t , s be any positive integers, and let R be an associative ring with identity. Suppose x t [ x n , y ] = [ x , y m ] y s 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. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t = s = 0 and m = n + 1 .

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:532436

DOI: 10.1155/S0161171284000569

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