Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties
Peter Danchev, Arash Javan, and Ahmad Moussavi
TL;DR
This paper introduces two new classes of rings, CSNC and NCUC, characterized by properties of their clean and nil-clean elements, expanding previous research in ring theory.
Contribution
It defines and explores properties of CSNC and NCUC rings, extending prior work on clean and nil-clean elements in rings.
Findings
Characterization of CSNC and NCUC rings
Extension of previous results by Calugareanu-Zhou and Cui-Danchev-Jin
New properties of clean and nil-clean elements in rings
Abstract
We define two types of rings, namely the so-called CSNC and NCUC that are those rings whose clean elements are strongly nil-clean, respectively, whose nil-clean elements are uniquely clean. Our results obtained in this paper somewhat expand these obtained by Calugareanu-Zhou in Mediterr. J. Math. (2023) and by Cui-Danchev-Jin in Publ. Math. Debrecen (2024), respectively.
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Taxonomy
TopicsRings, Modules, and Algebras