%0 Journal Article
%T Projective maximal submodules of extending regular modules
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Momtahan, E.
%D 2012
%\ 07/15/2012
%V 38
%N 2
%P 403-412
%! Projective maximal submodules of extending regular modules
%K continuous rings
%K extending rings
%K regular
rings
%K \aleph_0-self-injective rings
%R
%X We show that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of Dung and Smith. As another consequence, we observe thatevery right continuous ring, whose maximal right ideals areprojective, is semisimple Artinian. This generalizes some resultsof Osofsky and Karamzadeh. We also observe thatfour classes of rings, namely right $\aleph_0$-continuous rings,right continuous rings, right $\aleph_0$-continuous regular ringsand right continuous regular rings are not axiomatizable.
%U http://bims.iranjournals.ir/article_407_6a4d7f84d031275eb5d254f9f2871b8d.pdf