<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</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.

Generalizations of graded second submodules

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Generalizations of graded second submodules"}

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,...

Generalizations of graded second submodules

Published Online: Aug 26, 2021

Page range: 164 - 181

Received: Jul 29, 2020

DOI: https://doi.org/10.2478/ausm-2021-0009

Keywords
graded second submodule, graded ψ-second submodule, graded I-second submodule

© 2021 Peyman Ghiasvand et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalizations of graded second submodules

Published Online: Aug 26, 2021

Page range: 164 - 181

Received: Jul 29, 2020

DOI: https://doi.org/10.2478/ausm-2021-0009

Keywordsgraded second submodule, graded ψ-second submodule, graded I-second submodule

© 2021 Peyman Ghiasvand et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
graded second submodule, graded ψ-second submodule, graded I-second submodule