2003
DOI: 10.1070/sm2003v194n12abeh000788
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Multiplication modules over non-commutative rings

Abstract: It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If A 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 … Show more

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Cited by 14 publications
(7 citation statements)
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“…An R-semimodule M is said to be multiplication semimodule if for every subsemimodule N of M there exists an ideal I of R such that N = IM . Then N = (N : M )M [7,25,31].…”
Section: Preliminariesmentioning
confidence: 99%
“…An R-semimodule M is said to be multiplication semimodule if for every subsemimodule N of M there exists an ideal I of R such that N = IM . Then N = (N : M )M [7,25,31].…”
Section: Preliminariesmentioning
confidence: 99%
“…Let R be a ring. An R-module M is called a multiplication module if every submodule N of M has the form IM , for some ideal I of R, see [10]. We know that M is a multiplication R-module if and only if N = (N : R M )M , for every submodule N of M .…”
Section: Classical Weakly Prime Submodules Of a Multiplication Modulementioning
confidence: 99%
“…If R is a right top ring, then it is a quasi-duo ring (see Zhang et al, 2006, Corollary 2.8). Top modules and top rings have been investigated in McCasland et al (1997), Tuganbaev (2003, Zhang (1999), Zhang and Tong (2000), and Zhang et al (2004Zhang et al ( , 2006.…”
Section: Introductionmentioning
confidence: 99%