On M∗-Irresolute Topological Rings

Shallu Sharma, Shallu Sharma; Naresh Digra, Naresh Digra; Pooja Saproo, Pooja Saproo; Tsering Landol, Tsering Landol

doi:10.28924/2291-8639-21-2023-84

Research Article

On M∗-Irresolute Topological Rings

Shallu Sharma Shallu Sharma¹*
Naresh Digra Naresh Digra
Pooja Saproo Pooja Saproo
Tsering Landol Tsering Landol

a:1:{s:5:"en_US";s:19:"University of Jammu";}

* Corresponding author

Abstract

The main aim of this paper is to introduce and study the new notions namely M∗-irresolute topological rings and M∗-irresolute topological R-modules by virtue of M∗-open sets. Examples of an M∗-irresolute topological ring and module have been put forth. Further, we provide several fundamental properties and characterizations of M∗-irresolute topological rings and M∗-irresolute topological R-modules. In addition, we shall define boundedness in these two structures and present several results on them.

How to Cite

S. S. Shallu Sharma, N. D. Naresh Digra, P. S. Pooja Saproo, T. L. Tsering Landol, On M∗-Irresolute Topological Rings, Int. J. Anal. Appl. 21 (2023), 84. https://doi.org/10.28924/2291-8639-21-2023-84

BibTeX

@article{Sharma2023,
  author  = {Shallu Sharma, Shallu Sharma and Naresh Digra, Naresh Digra and Pooja Saproo, Pooja Saproo and Tsering Landol, Tsering Landol},
  title   = {On M∗-Irresolute Topological Rings},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {84},
  doi     = {10.28924/2291-8639-21-2023-84}
}

References

[1] V.I. Arnautov, M.I. Vodichar, A.V. Mikhalev, Introduction to The Theory of Topological Rings and Modules, Kishinev, Stiintsa, 1981.
[2] N. Bourbaki, Éléments de Mathématique, Topologie Générale, Hermann, Paris, (1965).
[3] M. Caldas, S. Jafari, M.M. Kovar, Some Properties of θ-Open Sets, Divul. Mat. 12 (2004), 161-169.
[4] A. Devika, A. Thilagavathi, M∗ -Open Sets in Topological Spaces, Int. J. Math. Appl. 4 (2016), 1-8.
[5] I.M. Gelfand, D.A. Raikov, G.E. Shilov, Commutative Normed Rings, Physmatizdt, 1960.
[6] A.Ya. Helemskii, Topologies in Banach and Topological Algebras, Moscow University, Moscow, 1986.
[7] A.Ya. Helemskii, Homology in Banach and Topological Algebras, Moscow University, Moscow, 1986.
[8] A.Ya. Helemskii, Banach and Normed Algebras, Nauka, 1989.
[9] I. Kaplansky, Topological Rings, Amer. J. Math. 69 (1947), 153-183. https://doi.org/10.2307/2371662.
[10] I. Kaplansky, Topological Rings, Bull. Amer. Math. Soc. 54 (1948), 809-826. https://doi.org/10.1090/s0002-9904-1948-09058-9.
[11] A.G. Kurosh, Lectures on General Algebra, Nauka, 1968.
[12] R.M. Latif, M–STAR–Irresolute Topological Vector Spaces, Int. J. Pure Math. 7 (2021), 20-36. https://doi.org/10.46300/91019.2020.7.4.
[13] M.A. Najmark, Normed Rings, Nauka, 1968.
[14] L.S. Pontryagin, Continuous Groups, Nauka, 1973.
[15] F. Szasz, On Topological Algebras and Rings, I, Mat. Zapok. 13 (1962), 256-278.
[16] F. Szasz, On Topological Algebras and Rings, II, Mat. Zapok. 14 (1963), 74-87.
[17] M. l. Ursul, Compact Rings and Their Generalizations, Kishinev, Stiinsta, 1991.
[18] S. Warner, Topological Rings, North-Holland Mathematics Studies, Vol. 178, North-Holland, (1993).