Research Article
BibTex RIS Cite

On S-primary submodules

Year 2022, Volume: 31 Issue: 31, 74 - 89, 17.01.2022
https://doi.org/10.24330/ieja.1058417

Abstract

Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module.
In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is shown that this
class of modules contains the family of primary (resp. $S$-prime) submodules properly.

References

  • R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715-1724.
  • D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
  • J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
  • Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
  • F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
  • R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, 1992.
  • C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33(1) (2007), 125-143.
  • R. L. McCasland and M. E. Moore, On radicals of submodules of finitely generated modules, Canad. Math. Bull., 29(1) (1986), 37-39.
  • R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803-1817.
  • M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, 1962.
  • E. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turkish J. Math., 43(2) (2019), 1036-1046.
  • F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016.
Year 2022, Volume: 31 Issue: 31, 74 - 89, 17.01.2022
https://doi.org/10.24330/ieja.1058417

Abstract

References

  • R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715-1724.
  • D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
  • J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
  • Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
  • F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
  • R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, 1992.
  • C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33(1) (2007), 125-143.
  • R. L. McCasland and M. E. Moore, On radicals of submodules of finitely generated modules, Canad. Math. Bull., 29(1) (1986), 37-39.
  • R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803-1817.
  • M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, 1962.
  • E. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turkish J. Math., 43(2) (2019), 1036-1046.
  • F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

H. Ansarı-toroghy This is me

S. S. Pourmortazavi This is me

Publication Date January 17, 2022
Published in Issue Year 2022 Volume: 31 Issue: 31

Cite

APA Ansarı-toroghy, H., & Pourmortazavi, S. S. (2022). On S-primary submodules. International Electronic Journal of Algebra, 31(31), 74-89. https://doi.org/10.24330/ieja.1058417
AMA Ansarı-toroghy H, Pourmortazavi SS. On S-primary submodules. IEJA. January 2022;31(31):74-89. doi:10.24330/ieja.1058417
Chicago Ansarı-toroghy, H., and S. S. Pourmortazavi. “On S-Primary Submodules”. International Electronic Journal of Algebra 31, no. 31 (January 2022): 74-89. https://doi.org/10.24330/ieja.1058417.
EndNote Ansarı-toroghy H, Pourmortazavi SS (January 1, 2022) On S-primary submodules. International Electronic Journal of Algebra 31 31 74–89.
IEEE H. Ansarı-toroghy and S. S. Pourmortazavi, “On S-primary submodules”, IEJA, vol. 31, no. 31, pp. 74–89, 2022, doi: 10.24330/ieja.1058417.
ISNAD Ansarı-toroghy, H. - Pourmortazavi, S. S. “On S-Primary Submodules”. International Electronic Journal of Algebra 31/31 (January 2022), 74-89. https://doi.org/10.24330/ieja.1058417.
JAMA Ansarı-toroghy H, Pourmortazavi SS. On S-primary submodules. IEJA. 2022;31:74–89.
MLA Ansarı-toroghy, H. and S. S. Pourmortazavi. “On S-Primary Submodules”. International Electronic Journal of Algebra, vol. 31, no. 31, 2022, pp. 74-89, doi:10.24330/ieja.1058417.
Vancouver Ansarı-toroghy H, Pourmortazavi SS. On S-primary submodules. IEJA. 2022;31(31):74-89.