Classical and strongly classical n-absorbing second submodules

Document Type : Research Paper

Author

Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Abstract

Let R be a commutative ring with identity and M be an R-module. The main purpose of this paper is to introduce and investigate the notion of classical and strongly classical n-absorbing second submodules as a dual notion of classical n-absorbing submodules. We obtain some basic properties of these classes of modules.

Keywords

References

  1. D. F. Anderson, A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra, 39 (2011), 1646-1672.
  2. H. Ansari-Toroghy, F. Farshadifar, Classical and strongly classical 2-absorbing second submodules, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., (1) 69 (2020), 123-136.
  3.  H. Ansari-Toroghy, F. Farshadifar, On the dual notion of prime radicals of submodules, Asian Eur. J. Math., (2) 6 (2013), 1350024.
  4.  H. Ansari-Toroghy, F. Farshadifar, Some generalizations of second submodules, Palest. J. Math., (2) 8 (2019), 1-10.
  5.  H. Ansari-Toroghy, F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math., (4) 11 (2007), 1189-1201.
  6.  H. Ansari-Toroghy, F. Farshadifar, The dual notion of some generalizations of prime submodules, Comm. Algebra, 39 (2011), 2396-2416.
  7.  H. Ansari-Toroghy, F. Farshadifar, S. Maleki-Roudposhti, n-absorbing and strongly n-absorbing second submodules, Bol. Soc. Parana. Mat., (1) 39 (2021), 9-22.
  8.  H. Ansari-Toroghy, F. Farshadifar, S. S. Pourmortazavi, On the P-interiors of submodules of Artinian modules, Hacet. J. Math. Stat., (3) 45 (2016), 675-682.
  9.  A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
  10.  A. Barnard, Multiplication modules, J. Algebra, 71 (1981), 174-178.
  11.  S. Ceken, M. Alkan, P.F. Smith, The dual notion of the prime radical of a module, J. Algebra, 392 (2013), 265-275.
  12.  A. Y. Darani, F. Soheilnia, On n-absorning submodules, Math. Commun., 17 (2012), 547-557.
  13. J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
  14.  L. Fuchs, W. Heinzer, B. Olberding, Commutative ideal theory without  niteness conditions: Irreducibility in the quotient  eld, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math. 249 (2006), 121-145.
  15.  N. Groenewaldon, Principally right 2-absorbing primary and weakly 2-absorbing primary ideals, J. Algebra Relat. Topics, (1) 9 (2021), 47-67.
  16.  I. Kaplansky, Commutative rings, University of Chicago Press, 1978.
  17. R. Nikandish, M. J. Nikmehr, A. Yassine, On classical n-absorbing submodules, Le Matematiche, (2) 74 (2019), 301-320.
  18.  P. Quartararo, H. S. Butts, Finite unions of ideals and modules, Proc. Amer. Math. Soc., 52 (1975), 91-96.
  19. S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37(2001), 273-278.
  20. S. Yassemi, The dual notion of the cyclic modules, Kobe. J. Math., 15 (1998), 41-46.
Journal of Algebra and Related Topics
Volume 10, Issue 2
December 2022
Pages 69-88

Files

Share

How to cite

Statistics