MINIMAL SUBMODULES GRAPH OF MODULES OVER COMMUTATIVE RINGS

Dwi Mifta Mahanani; Dewi Ismiarti; Syaiful Anam

doi:10.24330/ieja.1777583

MINIMAL SUBMODULES GRAPH OF MODULES OVER COMMUTATIVE RINGS

Dwi Mifta Mahanani^*
, Dewi Ismiarti
, Syaiful Anam

^*Corresponding author for this work

Faculty of Mathematics and Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M, denoted by Γ_min(M), in which the vertex set is the set of nonzero proper submodules of M. Two distinct vertices A and B are adjacent provided that A ∩ B is a minimal submodule of M. In this study, we associate some properties of the graph from the properties of module and vice versa. Moreover, if we have an R-module homomorphism from M to M′, we compare some invariant numbers and properties of Γ_min(M) and Γ_min(M′).

Original language	English
Pages (from-to)	184-196
Number of pages	13
Journal	International Electronic Journal of Algebra
Volume	39
Issue number	39
DOIs	https://doi.org/10.24330/ieja.1777583
Publication status	Published - 10 Jan 2026

Keywords

invariant number
Minimal submodule
module homomorphism

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10.24330/ieja.1777583

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abstract = "Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M, denoted by Γmin(M), in which the vertex set is the set of nonzero proper submodules of M. Two distinct vertices A and B are adjacent provided that A ∩ B is a minimal submodule of M. In this study, we associate some properties of the graph from the properties of module and vice versa. Moreover, if we have an R-module homomorphism from M to M′, we compare some invariant numbers and properties of Γmin(M) and Γmin(M′).",

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AU - Anam, Syaiful

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Y1 - 2026/1/10

N2 - Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M, denoted by Γmin(M), in which the vertex set is the set of nonzero proper submodules of M. Two distinct vertices A and B are adjacent provided that A ∩ B is a minimal submodule of M. In this study, we associate some properties of the graph from the properties of module and vice versa. Moreover, if we have an R-module homomorphism from M to M′, we compare some invariant numbers and properties of Γmin(M) and Γmin(M′).

AB - Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M, denoted by Γmin(M), in which the vertex set is the set of nonzero proper submodules of M. Two distinct vertices A and B are adjacent provided that A ∩ B is a minimal submodule of M. In this study, we associate some properties of the graph from the properties of module and vice versa. Moreover, if we have an R-module homomorphism from M to M′, we compare some invariant numbers and properties of Γmin(M) and Γmin(M′).

KW - invariant number

KW - Minimal submodule

KW - module homomorphism

UR - https://www.scopus.com/pages/publications/105030717234

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DO - 10.24330/ieja.1777583

M3 - Article

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EP - 196

JO - International Electronic Journal of Algebra

JF - International Electronic Journal of Algebra

IS - 39

ER -

MINIMAL SUBMODULES GRAPH OF MODULES OVER COMMUTATIVE RINGS

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Keywords

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