On M∗-Irresolute Topological Rings

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Shallu Sharma, Naresh Digra, Pooja Saproo, Tsering Landol

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.

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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).