Open AccessCOMMUTATIVITY OF RIGHT $S$-UNITAL RINGS UNDER SOME POLYNOMIAL CONSTRAINTS
Author(s) -
Mohammad Ashraf,
Murtaza A. Quadri,
V. W. Jacob
Publication year - 1993
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.24.1993.4470
Subject(s) - unital , mathematics , polynomial ring , ring (chemistry) , commutative property , polynomial , commutative ring , combinatorics , discrete mathematics , pure mathematics , algebra over a field , mathematical analysis , chemistry , organic chemistry
In the present paper we discuss the commutativity of certain rings, namely rings with unity 1 and right s-unital rings under each of the following conditions: \[ (P1)[yx^m - x^nf (y), x] = 0, \quad (P1)^*[yx^m - f (y)x^n, x] = 0, \]where $m$, $n$ are fixed non-negative integers and $f(x)$ is a polynomial in $X^2\mathbb{Z}(X)$ varying with the pair of ring elements $x$, $y$. Further, the results have been extended to the case when $m$ and $n$ depend on the choice of $x$ and $y$ and the ring satisfies the Chacron's condition.