On Prime Spectrums of Commutative Rings |
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| Authors: | Dancheng Lu Weihong Yu |
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| Institution: | 1. Department of Mathematics , Suzhou University , Suzhou, China ludancheng@suda.edu.cn;3. Hohai University , Changzhou, China |
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| Abstract: | We show that π-regular rings and clean rings can be completely characterized by topological properties of their prime spectrums respectively. In addition, we give some applications of those result. Among others, we improve the main result of Samei (2004
Samei , K. ( 2004 ). Clean elements in commutative reduced rings . Comm. Algebra 32 ( 9 ): 3479 – 3486 . CSA] CROSSREF] Taylor &; Francis Online], Web of Science ®] , Google Scholar]) and give a new criterion for a clean ring that a commutative ring is clean if and only if idempotents lifts modulo every radical ideal. |
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| Keywords: | Clean rings Regular rings Spectrum Strongly zero-dimensional Zero-dimensional |
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