On graded primary-like submodules of graded modules over graded commutative rings
نویسندگان
چکیده
Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of primary-like submodules as new generalization primary ideals give some basic results about modules. Special attention has been paid, when satisfies gr-primeful property, to find extra properties these submodules.
منابع مشابه
Graded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
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ژورنال
عنوان ژورنال: Proyecciones
سال: 2021
ISSN: ['0716-0917', '0717-6279']
DOI: https://doi.org/10.22199/issn.0717-6279-3467