TY - JOUR
ID - 407
TI - Projective maximal submodules of extending regular modules
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Momtahan, E.
AD - Yasouj University
Y1 - 2012
PY - 2012
VL - 38
IS - 2
SP - 403
EP - 412
KW - continuous rings
KW - extending rings
KW - regular
rings
KW - \aleph_0-self-injective rings
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_407.html
L1 - http://bims.iranjournals.ir/article_407_6a4d7f84d031275eb5d254f9f2871b8d.pdf
ER -