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- W1567890158 abstract "Let R be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm's properties for submodules of a nitely generated faithful multiplication R- module (see (8), (12) and (3)). Throughout this paper all rings will be commutative with identity and all mod- ules will be unitary. If R is a ring and N is a submodule of an R-module M, the ideal fr 2 R : rM Ng will be denoted by (N : M). Then (0 : M) is the annihilator of M, Ann(M). An R-module M is called a multiplication module if for each submodule N of M, N = IM for some ideal I of R. In this case we can take I = (N : M). Clearly, M is a multiplication module if and only if for each m 2 M, Rm = (Rm : M)M (see (6)). For an R-module M, we dene the ideal (M) = P m2M (Rm : M). If M is multiplication then M = P m2M Rm = P m2M (Rm : M)M = ( P m2M (Rm : M))M = (M)M." @default.
- W1567890158 created "2016-06-24" @default.
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- W1567890158 date "2004-01-01" @default.
- W1567890158 modified "2023-09-24" @default.
- W1567890158 title "MULTIPLICATION MODULES AND RELATED RESULTS" @default.
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