Generalizing unit-regular rings and special clean elements

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-05-0069

Keywords:

Unit-regular rings, Clean rings, Special clean elements, Weakly clean rings, Weakly unit-regular rings

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) ?-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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Published

2020-10-01

How to Cite

[1]
P. V. Danchev, “Generalizing unit-regular rings and special clean elements”, Proyecciones (Antofagasta, On line), vol. 39, no. 5, pp. 1123-1135, Oct. 2020.

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Artículos