On idempotent reflexive rings. (English) Zbl 1120.16004

Kim, Jin Yong; Baik, Jong Uk

Kyungpook Math. J. 46, No. 4, 597-601 (2006).

Summary: We introduce the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings.

MSC:

16D50	Injective modules, self-injective associative rings
16E50	von Neumann regular rings and generalizations (associative algebraic aspects)
16D25	Ideals in associative algebras

Keywords:

idempotent reflexive rings; HI-rings; von Neumann regular right self-injective rings; p-injective modules; weakly regular rings