نجمه دهقانی

Von-Neumman regular rings have been extensively studied in the literature. There are various module generalizations of the regular rings. An R-module M is called (strongly, unit-)endoregular if its endomorphism ring is a (strongly, unit-)regular ring, respectively. It is shown that when the strongly endoregular property is inherited by direct summands and direct sums. Besides, we show that semisimple Artinian rings are precisely the ones over which every nitely generated module is (unit-)endoregular. We also give a characterization of rings R whose every finitely cogenerated injective R-module is endoregular. This work is a preliminary report on our going research on this topi