International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 294301, 8 pages
Research Article

Left 𝑊 𝑀 𝐶 2 Rings

School of Mathematics, Yangzhou University, Yangzhou 225002, China

Received 12 January 2011; Revised 3 May 2011; Accepted 9 May 2011

Academic Editor: Frank Werner

Copyright © 2011 Junchao Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce in this paper the concept of left 𝑊 𝑀 𝐶 2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left 𝐻 𝐼 rings can be extended to left 𝑊 𝑀 𝐶 2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on strongly regular rings.