Research Article
BibTex RIS Cite

$\psi$-SECONDARY SUBMODULES OF A MODULE

Year 2020, , 77 - 87, 07.01.2020
https://doi.org/10.24330/ieja.662963

Abstract

Let $R$ be a commutative ring with identity and $M$ be an $R$-module. Let $\psi : S(M)\rightarrow S(M) \cup \{\emptyset \}$ be a function, where $S(M)$ denote the set of all submodules of $M$. The main purpose of this paper is to introduce and investigate the notion of $\psi$-secondary submodules of an $R$-module $M$ as a generalization of secondary submodules of $M$.

References

  • D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2) (2008), 686-696.
  • H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication mod- ules, Taiwanese J. Math., 11(4) (2007), 1189-1201.
  • H. Ansari-Toroghy, F. Farshadifar, S. S. Pourmortazavi and F. Khaliphe, On secondary modules, Int. J. Algebra, 6(16) (2012), 769-774.
  • M. Bataineh and S. Kuhail, Generalizations of primary ideals and submodules, Int. J. Contemp. Math. Sci., 6(17) (2011), 811-824.
  • J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
  • F. Farshadifar and H. Ansari-Toroghy, -second submodules of a module, sub- mitted.
  • L. Fuchs, W. Heinzer and B. Olberding, Commutative ideal theory without niteness conditions: Irreducibility in the quotient led, in: Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math., Chapman & Hall/CRC, Boca Raton, FL, 249 (2006), 121-145.
  • I. G. Macdonald, Secondary representation of modules over a commutative ring, Symposia Mathematica (Convegno di Algebra Commutativa, INDAM, Rome, 1971), Academic Press, London, XI (1973), 23-43.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37(4) (2001), 273-278.
  • N. Zamani, phi-prime submodules, Glasg. Math. J., 52(2) (2010), 253-259.
Year 2020, , 77 - 87, 07.01.2020
https://doi.org/10.24330/ieja.662963

Abstract

References

  • D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2) (2008), 686-696.
  • H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication mod- ules, Taiwanese J. Math., 11(4) (2007), 1189-1201.
  • H. Ansari-Toroghy, F. Farshadifar, S. S. Pourmortazavi and F. Khaliphe, On secondary modules, Int. J. Algebra, 6(16) (2012), 769-774.
  • M. Bataineh and S. Kuhail, Generalizations of primary ideals and submodules, Int. J. Contemp. Math. Sci., 6(17) (2011), 811-824.
  • J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
  • F. Farshadifar and H. Ansari-Toroghy, -second submodules of a module, sub- mitted.
  • L. Fuchs, W. Heinzer and B. Olberding, Commutative ideal theory without niteness conditions: Irreducibility in the quotient led, in: Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math., Chapman & Hall/CRC, Boca Raton, FL, 249 (2006), 121-145.
  • I. G. Macdonald, Secondary representation of modules over a commutative ring, Symposia Mathematica (Convegno di Algebra Commutativa, INDAM, Rome, 1971), Academic Press, London, XI (1973), 23-43.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37(4) (2001), 273-278.
  • N. Zamani, phi-prime submodules, Glasg. Math. J., 52(2) (2010), 253-259.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

F. Farshadifar This is me

H. Ansari-toroghy This is me

Publication Date January 7, 2020
Published in Issue Year 2020

Cite

APA Farshadifar, F., & Ansari-toroghy, H. (2020). $\psi$-SECONDARY SUBMODULES OF A MODULE. International Electronic Journal of Algebra, 27(27), 77-87. https://doi.org/10.24330/ieja.662963
AMA Farshadifar F, Ansari-toroghy H. $\psi$-SECONDARY SUBMODULES OF A MODULE. IEJA. January 2020;27(27):77-87. doi:10.24330/ieja.662963
Chicago Farshadifar, F., and H. Ansari-toroghy. “$\psi$-SECONDARY SUBMODULES OF A MODULE”. International Electronic Journal of Algebra 27, no. 27 (January 2020): 77-87. https://doi.org/10.24330/ieja.662963.
EndNote Farshadifar F, Ansari-toroghy H (January 1, 2020) $\psi$-SECONDARY SUBMODULES OF A MODULE. International Electronic Journal of Algebra 27 27 77–87.
IEEE F. Farshadifar and H. Ansari-toroghy, “$\psi$-SECONDARY SUBMODULES OF A MODULE”, IEJA, vol. 27, no. 27, pp. 77–87, 2020, doi: 10.24330/ieja.662963.
ISNAD Farshadifar, F. - Ansari-toroghy, H. “$\psi$-SECONDARY SUBMODULES OF A MODULE”. International Electronic Journal of Algebra 27/27 (January 2020), 77-87. https://doi.org/10.24330/ieja.662963.
JAMA Farshadifar F, Ansari-toroghy H. $\psi$-SECONDARY SUBMODULES OF A MODULE. IEJA. 2020;27:77–87.
MLA Farshadifar, F. and H. Ansari-toroghy. “$\psi$-SECONDARY SUBMODULES OF A MODULE”. International Electronic Journal of Algebra, vol. 27, no. 27, 2020, pp. 77-87, doi:10.24330/ieja.662963.
Vancouver Farshadifar F, Ansari-toroghy H. $\psi$-SECONDARY SUBMODULES OF A MODULE. IEJA. 2020;27(27):77-8.