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Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties (2401.02189v1)
Published 4 Jan 2024 in math.RA and math.RT
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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