Open AccessCOMMUTATIVITY AND DECOMPOSITION FOR NEAR RINGS
Author(s) -
Hamza A. S. Abujabal
Publication year - 1997
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.28.1997.4325
Subject(s) - mathematics , integer (computer science) , decomposition , class (philosophy) , commutative property , ring (chemistry) , combinatorics , commutative ring , decomposition theorem , discrete mathematics , chemistry , computer science , organic chemistry , artificial intelligence , programming language
Let $R$ be a distributively generated (d.g) near ring satisfy one of the following condit ions. (*) For each $x$, $y$ in $R$, there exists a positive integer $n =n(x,y)$ such that $xy =(yx)^n$.(**) For each $x$, $y$ in $R$, there exist positive integers $m = m(x,y)$ and $n = n(x,y)$ for which $xy = y^m x^n$. In [2], Bell proved the commutativity of $R$ satisfying (*) or (**) under appropriate additional hypothesis. In this paper, we generalize the above properties for wider class of near rings known as D-near rings. Also we provide an example for justification of our results. Furthermore, we give a decomposition Theorem for near rings satisfying (**).