Generalizing unit-regular rings and special clean elements
Abstract As a strengthening of the definition of weakly clean rings, given by Šter in J. Algebra (2014), and as a common generalization of the classical unit-regular rings, we define and investigate the class of socalled weakly unit-regular rings as those rings R for which, for every element a ∈ R, there exist a unit u and an idempotent e such that a − u − e ∈ (1 − e)Ra with aR ∩ eR = {0}. Some more exotic relationships with the well-known classes of clean, nil-clean and (strongly) π-regular rings are demonstrated as well. In particular, an elementwise extension of the so-called ”special clean elements” by Khurana et al. in J. Algebra & Appl. (2020) is also processed.
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| Main Author: | |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501123 |
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