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  • Special clean elements in rings
    Khurana, Dinesh ...
    A clean decomposition ▫$a = e + u$▫ in a ring ▫$R$▫ (with idempotent ▫$e$▫ and unit ▫$u$▫) is said to be special if ▫$aR \cap eR = 0$▫. We show that this is a left-right symmetric condition. Special ... clean elements (with such decompositions) exist in abundance, and are generally quite accessible to computations. Besides being both clean and unit-regular, they have many remarkable properties with respect to element-wise operations in rings. Several characterizations of special clean elements are obtained in terms of exchange equations, Bott-Duffin invertibility, and unit-regular factorizations. Such characterizations lead to some interesting constructions of families of special clean elements. Decompositions that are both special clean and strongly clean are precisely spectral decompositions of the group invertible elements. The paper also introduces a natural involution structure on the set of special clean decompositions, and describes the fixed point set of this involution.
    Source: Journal of algebra and its applications. - ISSN 0219-4988 (Vol. 19, no. 11, 2020, art. 2050208 (27 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2020
    Language - english
    COBISS.SI-ID - 58246403

    Link(s):

    https://www.worldscientific.com/doi/abs/10.1142/S0219498820502084
    DOI

source: Journal of algebra and its applications. - ISSN 0219-4988 (Vol. 19, no. 11, 2020, art. 2050208 (27 str.))

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