二阶子模的概化

Pub Date : 2021-08-01 DOI:10.2478/ausm-2021-0009

P. Ghiasvand, F. Farzalipour

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引用次数: 0

摘要

摘要设G是具有恒等e的群，设R是一个分级环，I是R的分级理想，M是一个G分级R模。设ψ: Sgr(M)→Sgr(M)∪{∅}是一个函数，其中Sgr(M)表示M的所有渐变子模的集合。本文引入并研究了渐变r模的渐变ψ -秒子模和渐变i -秒子模的概念，它们是M的渐变第二子模的推广，并研究了这类渐变模的一些性质。

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Generalizations of graded second submodules

Abstract Let G be a group with identity e. Let R be a graded ring, I a graded ideal of R and M be a G-graded R-module. Let ψ: Sgr(M) → S gr(M) ∪ {∅} be a function, where Sgr(M) denote the set of all graded submodules of M. In this article, we introduce and study the concepts of graded ψ -second submodules and graded I-second submodules of a graded R-module which are generalizations of graded second submodules of M and investigate some properties of this class of graded modules.

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