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ON THE STRONGLY ANNIHILATING-SUBMODULE GRAPH OF A MODULE

Year 2022, Volume: 51 Issue: 2, 443 - 454, 01.04.2022
https://doi.org/10.15672/hujms.810976

Abstract

References

  • [1] G. Aalipour, S. Akbari, M. Behboodi, R. Nikandish, M.J. Nikmehr and F. Shaveisi, The classification of the annihilating-ideal graphs of commutative rings, Algebra Col- loq. 21 (2), 249-256, 2014.
  • [2] G. Aalipour, S. Akbari, R. Nikandish, M.J. Nikmehr and F. Shaveisi, On the coloring of the annihilating-ideal graph of a commutative ring, Discrete Math. 312, 2620-2626, 2012.
  • [3] S. Akbari, H.R. Maimani and S. Yassemi, When a zero-divisor graph is planar or a complete r-partite graph, J. Algebra, 270, 169-180, 2003.
  • [4] S. Akbari and A. Mohammadian, Zero-divisor graphs of non-commutative rings, J. Algebra, 296, 462-479, 2006.
  • [5] F. Aliniaeifard, M. Behboodi, E. Mehdi-nezhad and A.M. Rahimi, The annihilating- ideal graph of a commutative ring with respect to an ideal, Comm. Algebra , 42, 2269-2284, 2014.
  • [6] D.F. Anderson, R. Levy and J. Shapiro J, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra, 180, 221-241, 2003.
  • [7] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra , 217, 434-447, 1999.
  • [8] D.D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra Appl. 159, 500-514, 1993.
  • [9] H. Ansari-Toroghy and Sh. Habibi, The Zariski topology-graph of modules over com- mutative rings, Comm. Algebra 42, 3283-3296, 2014.
  • [10] H. Ansari-Toroghy and Sh. Habibi, The annihilating-submodule graph of modules over commutative rings II. Arab J. Math. 5, 187-194, 2016.
  • [11] H. Ansari-Toroghy and Sh. Habibi, The annihilating-submodule graph of modules over commutative rings, Math. Reports 20, 245-262, 2018.
  • [12] A. Azizi, Weakly prime submodule and prime submodule, Glasgow Math. J. 48, 343- 346, 2006.
  • [13] I. Beck, Coloring of commutative rings, J. Algebra 116, 208-226, 1988.
  • [14] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (4), 727-739, 2011.
  • [15] R. Beyranvand and A. Farzi-Safarabadi, The strongly annihilating-submodule graph of a module, Algebraic Struc. Appl. 7 (1), 83-99, 2020.
  • [16] R. Beyranvand and F. Rastgoo, Weakly second modules over noncommutative rings, Hacet. J. Math. Stat. 45 (5), 1355-1366, 2016.
  • [17] S. Ceken, M. Alkan and P.F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41, 83-98, 2013.
  • [18] F.R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commu- tative semigroup, Semigroup Forum, 65, 206-214, 2002.
  • [19] R. Diestel, Graph Theory. Electronic Edition, New York: Springer-Verlag Heidelberg 1997, 2000, 2005.
  • [20] N. Jafari Rad, S.H. Jafari and D.A. Mojdeh, On domination in zero-divisor graphs, Canad. Math. Bull. 56 (2), 407-411, 2013.
  • [21] T.Y. Lam Lectures on modules and rings, Graduate Texts in Math. New York Heidelberg-Berlin: Springer-Verlag 1999.
  • [22] D.A. Mojdeh and A.M. Rahimi, Dominating sets of some graphs associated to com- mutative rings, Comm. Algebra, 40, 3389-3396, 2012.
  • [23] R. Nikandish, H. Maimani and S. Kiani, Domination numer in the annihilating-ideal graphs of commutative rings, Publications De L’institut Math. 97 (111), 225-231, 2015.
  • [24] S. Safaeeyan, Annihilating submodule graph for modules, Trans. Comb. 7 (1), 1-12, 2018.
  • [25] S. Safaeeyan, M. Baziar and E. Momtahan, A generalization of the zero-divisor graph for modules, J. Korean Math. Soc. 51 (1), 87-98, 2014.
  • [26] L. Toth, Subgroups of finite abelian groups having rank two via Goursats lemma, Tatra Mt. Math. Publ. 59 (1), 93-103, 2014.

On the strongly annihilating-submodule graph of a module

Year 2022, Volume: 51 Issue: 2, 443 - 454, 01.04.2022
https://doi.org/10.15672/hujms.810976

Abstract

In this paper we continue to study the strongly annihilating-submodule graph. In addition to providing the more properties of this graph, we compare extensively the properties of this graph with the annihilating-submodule graph.

References

  • [1] G. Aalipour, S. Akbari, M. Behboodi, R. Nikandish, M.J. Nikmehr and F. Shaveisi, The classification of the annihilating-ideal graphs of commutative rings, Algebra Col- loq. 21 (2), 249-256, 2014.
  • [2] G. Aalipour, S. Akbari, R. Nikandish, M.J. Nikmehr and F. Shaveisi, On the coloring of the annihilating-ideal graph of a commutative ring, Discrete Math. 312, 2620-2626, 2012.
  • [3] S. Akbari, H.R. Maimani and S. Yassemi, When a zero-divisor graph is planar or a complete r-partite graph, J. Algebra, 270, 169-180, 2003.
  • [4] S. Akbari and A. Mohammadian, Zero-divisor graphs of non-commutative rings, J. Algebra, 296, 462-479, 2006.
  • [5] F. Aliniaeifard, M. Behboodi, E. Mehdi-nezhad and A.M. Rahimi, The annihilating- ideal graph of a commutative ring with respect to an ideal, Comm. Algebra , 42, 2269-2284, 2014.
  • [6] D.F. Anderson, R. Levy and J. Shapiro J, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra, 180, 221-241, 2003.
  • [7] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra , 217, 434-447, 1999.
  • [8] D.D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra Appl. 159, 500-514, 1993.
  • [9] H. Ansari-Toroghy and Sh. Habibi, The Zariski topology-graph of modules over com- mutative rings, Comm. Algebra 42, 3283-3296, 2014.
  • [10] H. Ansari-Toroghy and Sh. Habibi, The annihilating-submodule graph of modules over commutative rings II. Arab J. Math. 5, 187-194, 2016.
  • [11] H. Ansari-Toroghy and Sh. Habibi, The annihilating-submodule graph of modules over commutative rings, Math. Reports 20, 245-262, 2018.
  • [12] A. Azizi, Weakly prime submodule and prime submodule, Glasgow Math. J. 48, 343- 346, 2006.
  • [13] I. Beck, Coloring of commutative rings, J. Algebra 116, 208-226, 1988.
  • [14] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (4), 727-739, 2011.
  • [15] R. Beyranvand and A. Farzi-Safarabadi, The strongly annihilating-submodule graph of a module, Algebraic Struc. Appl. 7 (1), 83-99, 2020.
  • [16] R. Beyranvand and F. Rastgoo, Weakly second modules over noncommutative rings, Hacet. J. Math. Stat. 45 (5), 1355-1366, 2016.
  • [17] S. Ceken, M. Alkan and P.F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41, 83-98, 2013.
  • [18] F.R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commu- tative semigroup, Semigroup Forum, 65, 206-214, 2002.
  • [19] R. Diestel, Graph Theory. Electronic Edition, New York: Springer-Verlag Heidelberg 1997, 2000, 2005.
  • [20] N. Jafari Rad, S.H. Jafari and D.A. Mojdeh, On domination in zero-divisor graphs, Canad. Math. Bull. 56 (2), 407-411, 2013.
  • [21] T.Y. Lam Lectures on modules and rings, Graduate Texts in Math. New York Heidelberg-Berlin: Springer-Verlag 1999.
  • [22] D.A. Mojdeh and A.M. Rahimi, Dominating sets of some graphs associated to com- mutative rings, Comm. Algebra, 40, 3389-3396, 2012.
  • [23] R. Nikandish, H. Maimani and S. Kiani, Domination numer in the annihilating-ideal graphs of commutative rings, Publications De L’institut Math. 97 (111), 225-231, 2015.
  • [24] S. Safaeeyan, Annihilating submodule graph for modules, Trans. Comb. 7 (1), 1-12, 2018.
  • [25] S. Safaeeyan, M. Baziar and E. Momtahan, A generalization of the zero-divisor graph for modules, J. Korean Math. Soc. 51 (1), 87-98, 2014.
  • [26] L. Toth, Subgroups of finite abelian groups having rank two via Goursats lemma, Tatra Mt. Math. Publ. 59 (1), 93-103, 2014.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Reza Beyranvand 0000-0002-4113-4537

Ahadollah Farzı-safarabadı This is me

Publication Date April 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 2

Cite

APA Beyranvand, R., & Farzı-safarabadı, A. (2022). On the strongly annihilating-submodule graph of a module. Hacettepe Journal of Mathematics and Statistics, 51(2), 443-454. https://doi.org/10.15672/hujms.810976
AMA Beyranvand R, Farzı-safarabadı A. On the strongly annihilating-submodule graph of a module. Hacettepe Journal of Mathematics and Statistics. April 2022;51(2):443-454. doi:10.15672/hujms.810976
Chicago Beyranvand, Reza, and Ahadollah Farzı-safarabadı. “On the Strongly Annihilating-Submodule Graph of a Module”. Hacettepe Journal of Mathematics and Statistics 51, no. 2 (April 2022): 443-54. https://doi.org/10.15672/hujms.810976.
EndNote Beyranvand R, Farzı-safarabadı A (April 1, 2022) On the strongly annihilating-submodule graph of a module. Hacettepe Journal of Mathematics and Statistics 51 2 443–454.
IEEE R. Beyranvand and A. Farzı-safarabadı, “On the strongly annihilating-submodule graph of a module”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, pp. 443–454, 2022, doi: 10.15672/hujms.810976.
ISNAD Beyranvand, Reza - Farzı-safarabadı, Ahadollah. “On the Strongly Annihilating-Submodule Graph of a Module”. Hacettepe Journal of Mathematics and Statistics 51/2 (April 2022), 443-454. https://doi.org/10.15672/hujms.810976.
JAMA Beyranvand R, Farzı-safarabadı A. On the strongly annihilating-submodule graph of a module. Hacettepe Journal of Mathematics and Statistics. 2022;51:443–454.
MLA Beyranvand, Reza and Ahadollah Farzı-safarabadı. “On the Strongly Annihilating-Submodule Graph of a Module”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, 2022, pp. 443-54, doi:10.15672/hujms.810976.
Vancouver Beyranvand R, Farzı-safarabadı A. On the strongly annihilating-submodule graph of a module. Hacettepe Journal of Mathematics and Statistics. 2022;51(2):443-54.