On semi-topological rings

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DOI:

https://doi.org/10.26637/MJM0704/0028

Abstract

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 rings

Mathematics Subject Classification:

Mathematics
  • Shallu Sharma Department of Mathematics, University of Jammu, JK-180006, India.
  • Madhu Ram Department of Mathematics, University of Jammu, JK-180006, India.
  • Sahil Billawria Department of Mathematics, University of Jammu, JK-180006, India.
  • Tsering Landol Department of Mathematics, University of Jammu, JK-180006, India.
  • Pages: 808-812
  • Date Published: 01-10-2019
  • Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

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Published

01-10-2019

How to Cite

Shallu Sharma, Madhu Ram, Sahil Billawria, and Tsering Landol. “On Semi-Topological Rings”. Malaya Journal of Matematik, vol. 7, no. 04, Oct. 2019, pp. 808-12, doi:10.26637/MJM0704/0028.

Issue

Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

Section

Articles

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Copyright (c) 2019 MJM

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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