Minimal submodules graph of modules over commutative rings

Mahanani, Dwi Mifta, Ismiarti, Dewi and Anam, Syaiful (2025) Minimal submodules graph of modules over commutative rings. International Electronic Journal of Algebra. ISSN 1306-6048

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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 ′).

Item Type:	Journal Article
Keywords:	Minimal submodule; module homomorphism; invariant number
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Dewi Ismiarti
Date Deposited:	20 Oct 2025 11:17

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