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Almost graded multiplication and almost graded comultiplication modules

Bataineh Malik, Abu-Dawwas Rashid, Shtayat Jenan

Demonstratio Mathematica

2020

Vol. 53, nr 1

325--331

Let G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a ∈ h(R) satisfies AnnR (aM) = AnnR (M), then (0 :M a) = {0}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a ∈ h(R) satisfies AnnR (aM) = AnnR (M), then aM = M. We investigate several properties of these classes of graded modules.

Indecomposable weak multiplication modules over Dedekind domains

Atani S.

Demonstratio Mathematica

2008

Vol. 41, nr 1

33-43

Let R be a Dedekind domain. We classify all indecomposable weak multiplication R-modules and we establish a connection between the weak multiplicatin modules, the pure multiplication modules and the pure-injective modules over such domains.