@article { author = {Momtahan, E.}, title = {Projective maximal submodules of extending regular modules}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {38}, number = {2}, pages = {403-412}, year = {2012}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {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.}, keywords = {continuous rings,extending rings,regular rings,\aleph_0-self-injective rings}, url = {http://bims.iranjournals.ir/article_407.html}, eprint = {http://bims.iranjournals.ir/article_407_6a4d7f84d031275eb5d254f9f2871b8d.pdf} }