Open AccessA GENERALIZATION OF SOME COMMUTATIVITY THEOREMS FOR RINGS I
Author(s) -
H. A. S. Abujabal
Publication year - 1990
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.21.1990.4669
Subject(s) - mathematics , commutative property , generalization , unital , polynomial ring , identity (music) , commutative ring , ring (chemistry) , polynomial , discrete mathematics , pure mathematics , combinatorics , algebra over a field , mathematical analysis , chemistry , physics , organic chemistry , acoustics
In this paper we generalize some well-known commutativity theorems for rings as follows: Let $m > 1$, and $n$, $k$ be non-negative integers. Let $R$ be an $s$ - unital ring satisfying the polynomial identity $[x^ny- y^mx^k, x]=0$, for all $x,y\in R$. Then $R$ is commutative.