Exchange Rings with Artinian Primitive Factors |
| |
Authors: | Huanyin Chen |
| |
Institution: | (1) Department of Mathematics, Hunan Normal University, Changsha, 410006, P. R. China |
| |
Abstract: | We prove that every exchange ring with primitive factors Artinian is clean. Also, it is shown that for exchange rings with Artinian primitive factors, the following are equivalent: (1) Every element in R is a sum of two units. (2) There exist , U(R) such that + = 1. (3) R does not have Z / 2 Z as a homomorphic image. Finally, we prove that exchange ring R is strongly -regular if the Jacobson radical of any homomorphic image of R is T-nilpotent or locally nilpotent. These are generalizations of the corresponding results of A. Badawi, W. D. Burgess and P. Menal, Fisher and Snider, and J. Stock. |
| |
Keywords: | exchange ring clean ring unit and strongly -regularity" target="_blank">gif" alt="pgr" align="BASELINE" BORDER="0">-regularity |
本文献已被 SpringerLink 等数据库收录! |
|