Research Article Open Access

Remark on Bi-Ideals and Quasi-Ideals of Variants of Regular Rings

Samruam Baupradist1 and Ronnason Chinram1
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Journal of Mathematics and Statistics
Volume 7 No. 1, 2011, 78-80

DOI: https://doi.org/10.3844/jmssp.2011.78.80

Submitted On: 25 February 2011 Published On: 25 March 2011

How to Cite: Baupradist, S. & Chinram, R. (2011). Remark on Bi-Ideals and Quasi-Ideals of Variants of Regular Rings. Journal of Mathematics and Statistics, 7(1), 78-80. https://doi.org/10.3844/jmssp.2011.78.80

Abstract

Problem statement: Every quasi-ideal of a ring is a bi-ideal. In general, a bi-ideal of a ring need not be a quasi-ideal. Every bi-ideal of regular rings is a quasi-ideal, so bi-ideals and quasi-ideals of regular rings coincide. It is known that variants of a regular ring need not be regular. The aim of this study is to study bi-ideals and quasi-ideals of variants of regular rings. Approach: The technique of the proof of main theorem use the properties of regular rings and bi-ideals. Results: It shows that every bi-ideal of variants of regular rings is a quasi-ideal. Conclusion: Although the variant of regular rings need not be regular but every bi-ideal of variants of regular rings is a quasi-ideal.

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Keywords

  • Bi-ideals
  • quasi-ideals
  • variants
  • regular rings
  • BQ-rings