Open AccessCOMMUTATIVITY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS
Author(s) -
Hamza A. S. Abujabal,
Mohd. Shaikhul Ashraf
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.26.1995.4375
Subject(s) - mathematics , unital , integer (computer science) , commutative property , exponent , combinatorics , ring (chemistry) , commutative ring , discrete mathematics , pure mathematics , algebra over a field , chemistry , linguistics , philosophy , organic chemistry , computer science , programming language
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). Finally, the result is extended to the case when the exponent $m$ depends on the choice of $x$ and $y$.