Abstract:
It is proved that each submodule of a multiplication module over a regular ring
is a multiplicative module. If AA is a ring with commutative multiplication of right
ideals, then each projective right ideal is a multiplicative module, and a finitely generated
A-module M is a multiplicative module if and only if all its localizations
with respect to maximal right ideals of A are cyclic modules over the corresponding localizations of A. In addition, several known results on multiplication modules over
commutative rings are extended to modules over not necessarily commutative rings.
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