Some results on the strongly annihilating submodule graph of a module

Document Type : Research Paper

Authors

1 Department of Mathematics, Lorestan university, Khoramabad, Iran.

2 Department of Mathematics, Islamic Azad University, Khorramabad branch, Khoramabad, Iran.

Abstract

Let M be a module over a commutative ring R. We continue our study of strongly annihilating submodule graph SAG(M) introduced in [9]. In addition to providing the more properties of this graph, we introduce the subgraph SAG∗(M) of SAG(M) and compare the properties of SAG∗(M) with SAG(M) and AG(M) (the annihilating submodule graph
of M introduced in [5])

Keywords


[1] S. Akbari, H. R. Maimani and S. Yassemi, When a zero-divisor graph is planar or a complete r-partite graph, J. Algebra, 270 No. 1 (2003) 169-180.
[2] S. Akbari and A. Mohammadian, Zero-divisor graphs of non-commutative rings, J. Algebra, 296 No. 2 (2006) 462-479.
[3] H. Ansari-Toroghy and S. Habibi, The annihilating-submodule graph of modules over commutative rings, Math. Reports, 20 No. 70 (2018) 245-262.
[4] H. Ansari-Toroghy and S. Habibi, The Zariski topology-graph of modules over commutative rings, Comm. Algebra, 42 No. 8 (2014) 3283-3296.
[5] M. Behboodi and R. Beyranvand, Strong zero-divisor graphs of noncommutative rings, International J. Algebra, 2 No. 1 (2008) 25-44.
[6] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl., 10 No. 4 (2011) 727-739.
[7] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings II, J. Algebra Appl., 10 No. 4 (2011) 741-753.
[8] R. Beyranvand and A. Farzi-Safarabadi, On the Strongly annihilating-submodule graph of a module, Hacettepe J. Math. Stat., 51 No. 2 (2022) 443-454.
[9] F. R. Demeyer, T. McKezie and K. Schneider, The zero-divisor graph of a commutative semigroup, Semig. Forum, 65 (2002) 206-214.
[10] R. Diestel, Graph Theory, Electronic Edition, Springer-Verlag, Heidelberg, New York, 2005.
[11] A. Farzi-Safarabadi and R. Beyranvand, The Strongly annihilating-submodule graph of a module, ASTA, 7 No. 1 (2020) 83-99.
[12] T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.