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چکیده
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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
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