Remark on Bi-Ideals and Quasi-Ideals of Variants of Regular Rings
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Copyright: © 2020 Samruam Baupradist and Ronnason Chinram. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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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- regular rings