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A note on completeness and strongly clean rings |
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| Authors: | Alexander J. Diesl Thomas J. Dorsey Shelly Garg Dinesh Khurana |
| Affiliation: | 1. Department of Mathematics, Wellesley College, Wellesley, MA 02481, USA;2. Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121-1969, USA;3. Department of Mathematics, Indian Institute of Science Education and Research, Mohali-140306, India;4. Department of Mathematics, Panjab University, Chandigarh-160014, India |
| Abstract: | Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we investigate the classical problem of lifting idempotents, in order to consolidate and extend these results. Our main result is that if R is a ring which is complete with respect to an ideal I and if x is an element of R whose image in R/I is strongly π-regular, then x is strongly clean in R. This generalizes Theorem 2.1 of Chen and Zhou (2007) [9]. |
| Keywords: | 16U99 16E50 |
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