Commutativity of rings through a Streb's result期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Commutativity of rings through a Streb's result

Authors:

Institution:

(1) Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 30356, Jeddah –, 21477, Saudi Arabia

Abstract:

In this paper we investigate commutativity of rings with unity satisfying any one of the properties:

$\left\{ {{\text{1 - }}g\left( {yx^m } \right)} \right\}\left {yx^m - x^r f\left( {yx^m } \right)x^s ,x} \right]\left\{ {1 - h\left( {yx^m } \right)} \right\} = 0$

$\left\{ {{\text{1 - }}g\left( {yx^m } \right)} \right\}\left {x^m y - x^r f\left( {yx^m } \right)x^s ,x} \right]\left\{ {1 - h\left( {yx^m } \right)} \right\} = 0$

$y^t \left {x,y^n } \right] = g\left( x \right)\left {f\left( x \right),y} \right]h\left( x \right){\text{ and }}\left {x,y^n } \right]y^t = g\left( x \right)\left {f\left( x \right),y} \right]h\left( x \right)$

for some f(X) in $X^2 \mathbb{Z}\left X \right]$ and g(X), h(X) in $\mathbb{Z}\left X \right]$ where m

0, r

0, s

0, n > 0, t > 0 are non-negative integers. We also extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values. Further, under different appropriate constraints on commutators, commutativity of rings has been studied. These results generalize a number of commutativity theorems established recently.

Keywords:

commutators division rings factorsubrings polynomial identities torsion-free rings

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏