TWO ELEMENTARY COMMUTATIVITY THEOREMS FOR GENERALIZED BOOLEAN RINGS

VISHNU GUPTA

《International Journal of Mathematics and Mathematical Sciences》 1997卷 (1997/12) Pp. 409-411

https://doi.org/10.1155/S0161171297000549

摘要

In this paper we prove that if R is a ring with 1 as an identity element in which x^m-x^n ∈ Z(R) for all x ∈ R and fixed relatively prime positive integers m and n, one of which is even, then R is commutative. Also we prove that if R is a 2-torsion free ring with 1 in which (x^(2k))^(n+1)-(x^(2k))^n ∈ Z(R) for all x ∈ R and fixed positive integer n and non-negative integer k, then R is commutative.

關鍵字

Commutator ； 2-torsion free ring