Research Article
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Year 2024, Early Access, 1 - 15
https://doi.org/10.24330/ieja.1480269

Abstract

References

  • D. D. Anderson, T. Arabaci, U. Tekir and S. Koc, On S-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
  • A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
  • S. Baupradist and S. Asawasamrit, On fully-M-cyclic modules, J. Math. Res., 3(2) (2011), 23-26.
  • S. Baupradist and S. Asawasamrit, GW-principally injective modules and pseudo-GW-principally injective modules, Southeast Asian Bull. Math., 42 (2018), 521-529.
  • S. Baupradist, H. D. Hai and N. V. Sanh, On pseudo-p-injectivity, Southeast Asian Bull. Math., 35(1) (2011), 21-27.
  • S. Baupradist, H. D. Hai and N. V. Sanh, A general form of pseudo-p-injectivity, Southeast Asian Bull. Math., 35 (2011), 927-933.
  • A. Haghany and M. R. Vedadi, Modules whose injective endomorphisms are essential, J. Algebra, 243(2) (2001), 765-779.
  • V. Kumar, A. J. Gupta, B. M. Pandeya and M. K. Patel, M-sp-injective modules, Asian-Eur. J. Math., 5(1) (2012), 1250005 (11 pp).
  • S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Math. Soc. Lecture Note Series, 147, Cambridge Univ. Press, Cambridge, 1990.
  • W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  • M. K. Patel and S. Chase, FI-semi-injective modules, Palest. J. Math., 11(1) (2022), 182-190.
  • M. K. Patel, B. M. Pandeya, A. J. Gupta and V. Kumar, Quasi principally injective modules, Int. J. Algebra, 4 (2010), 1255-1259.
  • T. C. Quynh and N. V. Sanh, On quasi pseudo-GP-injective rings and modules, Bull. Malays. Math. Sci. Soc., 37(2) (2014), 321-332.
  • N. V. Sanh and K. P. Shum, Endomorphism rings of quasi principally injective modules, Comm. Algebra, 29(4) (2001), 1437-1443.
  • N. V. Sanh, K. P. Shum, S. Dhompongsa and S.Wongwai, On quasi-principally injective modules, Algebra Colloq., 6(3) (1999), 269-276.
  • W. M. Xue, On Morita duality, Bull. Austral. Math. Soc., 49(1) (1994), 35-45.
  • Z. Zhu, Pseudo QP-injective modules and generalized pseudo QP-injective modules, Int. Electron. J. Algebra, 14 (2013), 32-43.

$S$-$M$-cyclic submodules and some applications

Year 2024, Early Access, 1 - 15
https://doi.org/10.24330/ieja.1480269

Abstract

In this paper, we introduce the notion of $S$-$M$-cyclic submodules, which is a generalization of the notion of $M$-cyclic submodules. Let $M, N$ be right $R$-modules and $S$ be a multiplicatively closed subset of a ring $R$. A submodule $A$ of $N$ is said to be an $S$-$M$-cyclic submodule, if there exist $s\in S$ and $f \in Hom_R(M,N)$ such that $As \subseteq f(M) \subseteq A$. Besides giving many properties of $S$-$M$-cyclic submodules, we generalize some results on $M$-cyclic submodules to $S$-$M$-cyclic submodules. Furthermore, we generalize some properties of principally injective modules and pseudo-principally injective modules to $S$-principally injective modules and $S$-pseudo-principally injective modules, respectively. We study the transfer of this notion to various contexts of these modules.

References

  • D. D. Anderson, T. Arabaci, U. Tekir and S. Koc, On S-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
  • A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
  • S. Baupradist and S. Asawasamrit, On fully-M-cyclic modules, J. Math. Res., 3(2) (2011), 23-26.
  • S. Baupradist and S. Asawasamrit, GW-principally injective modules and pseudo-GW-principally injective modules, Southeast Asian Bull. Math., 42 (2018), 521-529.
  • S. Baupradist, H. D. Hai and N. V. Sanh, On pseudo-p-injectivity, Southeast Asian Bull. Math., 35(1) (2011), 21-27.
  • S. Baupradist, H. D. Hai and N. V. Sanh, A general form of pseudo-p-injectivity, Southeast Asian Bull. Math., 35 (2011), 927-933.
  • A. Haghany and M. R. Vedadi, Modules whose injective endomorphisms are essential, J. Algebra, 243(2) (2001), 765-779.
  • V. Kumar, A. J. Gupta, B. M. Pandeya and M. K. Patel, M-sp-injective modules, Asian-Eur. J. Math., 5(1) (2012), 1250005 (11 pp).
  • S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Math. Soc. Lecture Note Series, 147, Cambridge Univ. Press, Cambridge, 1990.
  • W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  • M. K. Patel and S. Chase, FI-semi-injective modules, Palest. J. Math., 11(1) (2022), 182-190.
  • M. K. Patel, B. M. Pandeya, A. J. Gupta and V. Kumar, Quasi principally injective modules, Int. J. Algebra, 4 (2010), 1255-1259.
  • T. C. Quynh and N. V. Sanh, On quasi pseudo-GP-injective rings and modules, Bull. Malays. Math. Sci. Soc., 37(2) (2014), 321-332.
  • N. V. Sanh and K. P. Shum, Endomorphism rings of quasi principally injective modules, Comm. Algebra, 29(4) (2001), 1437-1443.
  • N. V. Sanh, K. P. Shum, S. Dhompongsa and S.Wongwai, On quasi-principally injective modules, Algebra Colloq., 6(3) (1999), 269-276.
  • W. M. Xue, On Morita duality, Bull. Austral. Math. Soc., 49(1) (1994), 35-45.
  • Z. Zhu, Pseudo QP-injective modules and generalized pseudo QP-injective modules, Int. Electron. J. Algebra, 14 (2013), 32-43.
There are 17 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Samruam Baupradist

Early Pub Date May 7, 2024
Publication Date
Submission Date January 9, 2024
Acceptance Date April 2, 2024
Published in Issue Year 2024 Early Access

Cite

APA Baupradist, S. (2024). $S$-$M$-cyclic submodules and some applications. International Electronic Journal of Algebra1-15. https://doi.org/10.24330/ieja.1480269
AMA Baupradist S. $S$-$M$-cyclic submodules and some applications. IEJA. Published online May 1, 2024:1-15. doi:10.24330/ieja.1480269
Chicago Baupradist, Samruam. “$S$-$M$-Cyclic Submodules and Some Applications”. International Electronic Journal of Algebra, May (May 2024), 1-15. https://doi.org/10.24330/ieja.1480269.
EndNote Baupradist S (May 1, 2024) $S$-$M$-cyclic submodules and some applications. International Electronic Journal of Algebra 1–15.
IEEE S. Baupradist, “$S$-$M$-cyclic submodules and some applications”, IEJA, pp. 1–15, May 2024, doi: 10.24330/ieja.1480269.
ISNAD Baupradist, Samruam. “$S$-$M$-Cyclic Submodules and Some Applications”. International Electronic Journal of Algebra. May 2024. 1-15. https://doi.org/10.24330/ieja.1480269.
JAMA Baupradist S. $S$-$M$-cyclic submodules and some applications. IEJA. 2024;:1–15.
MLA Baupradist, Samruam. “$S$-$M$-Cyclic Submodules and Some Applications”. International Electronic Journal of Algebra, 2024, pp. 1-15, doi:10.24330/ieja.1480269.
Vancouver Baupradist S. $S$-$M$-cyclic submodules and some applications. IEJA. 2024:1-15.