On semi-topological rings
Downloads
DOI:
https://doi.org/10.26637/MJM0704/0028Abstract
We introduce and study the semi-topological rings. Some examples of semi-topological rings are provided. We investigate some permanence properties of semi-topological rings. Along with other results, it is proved that translation of an open (resp. closed) set in a semi-topological ring is semi-open (resp. semi-closed), that multiplication of an open (resp. closed) set in a semi-topological ring by an invertible element of the ring is semi-open (resp. semi-closed). We also prove that any ring homomorphism between a semi-topological ring and a topological ring which is continuous at zero is semi-continuous everywhere.
Keywords:
Semi-open sets, semi-closed sets, semi-continuous mappings, semi-topological ringsMathematics Subject Classification:
Mathematics- Pages: 808-812
- Date Published: 01-10-2019
- Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)
V.I. Arnautov, M.I. Vodinchar and A.V. Mikhalev, Introduction to the Theory of Topological Rings and Modules (Shtiinca, Kishinev, 1981) (in Russian).
S.G. Crossley and S.K. Hildebrand, Semi-closure, Texas J. Sci., 22 (1971), 99-112.
I. Kaplansky, Topological rings, Amer. J. Math., 69(1947), $153-182$.
I. Kaplansky, Dual rings, Ann. of Math., 49 (1948), 689701.
I. Kaplansky, Topological rings, Bull. Amer. Math. Soc., $54(1948), 809-826$
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
T.M. Nour, A Note on some Applications of Semi-open sets, Int. J. Math. and Math. Sci., 21(1)(1998), 205-207.
M. Ram, S. Sharma, S. Billawria and T. Landol, On $alpha$-Irresolute Topological Rings, International Journal of Mathematics Trends and Technology, 65(2) (2019), 1-5.
H.M.M. Salih, On Irresolute Topological Rings, J. Adv. Stud. Topol., 9(2) (2018), 130-134.
S. Warner, Topological Rings, North Holland, 1993.
- NA
Similar Articles
- K. Sreeram Reddy, Unsteady thermal boundary layer flows of vertical plate through numerical techniques , Malaya Journal of Matematik: Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.