Commutativity theorems for rings with constraints on commutators

Hamza A. S. Abujabal

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-6

Abstract:

In this paper, we generalize some well-known commutativity theorems for associative rings as follows: Let n > 1 , m , s , and t be fixed non-negative integers such that s ≠ m − 1 , or t ≠ n − 1 , and let R be a ring with unity 1 satisfying the polynomial identity y s [ x n , y ] = [ x , y m ] x t for all y ∈ R . Suppose that (i) R has Q ( n ) (that is n [ x , y ] = 0 implies [ x , y ] = 0 ); (ii) the set of all nilpotent elements of R is central for t > 0 , and (iii) the set of all zero-divisors of R is also central for t > 0 . Then R is commutative. If Q ( n ) is replaced by m and n are relatively prime positive integers, then R is commutative if extra constraint is given. Other related commutativity results are also obtained.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:170641

DOI: 10.1155/S0161171291000911

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