Some properties of the graph of modules with respect to a first dual homomorphism

Document Type : Original Paper

Authors

1 Yasouj University

2 Not sure

10.22055/jamm.2025.47571.2298

Abstract

For an R-module M and f ∈ M∗ = Hom(M, R), let Zf(M) and Regf(M) be the sets of all zero-divisors elements and regular elements of M with re- spect to f, respectively. In this paper, we introduce the total graph of M with respect to f, denoted by T(Γf(M)), which is the graph with all the elements M as vertices, and for distinct elements m, n ∈ M, m and n are adjacent and only if m + n ∈ Zf(M). We also study the subgraphs Z(Γf(M)) and Reg(Γf(M)) with vertices Zf(M) and Regf(M), respectively.

Keywords

Main Subjects


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