Some graphs related to submodules of a module
Commutative Algebra
2025-05-15 v1
Abstract
Let R be a commutative ring with identity and M be an R-module. In this paper, we introduce and investigate the second submodule intersection graph SSI(M) of M with vertices are nonzero proper submodules of M and two distinct vertices N and K are adjacent if and only if is a second submodule of M. Also, we introduce and consider the prime submodule sum graph PSS(M) of M with vertices are non-zero proper submodules of M and two distinct vertices N and K are adjacent if and only if N + K is a prime submodule of M.
Cite
@article{arxiv.2505.09448,
title = {Some graphs related to submodules of a module},
author = {Faranak Farshadifar},
journal= {arXiv preprint arXiv:2505.09448},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2406.11387