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Sums of commuting potent and nilpotent elements in rings

    https://doi.org/10.1142/S021949882350113XCited by:4 (Source: Crossref)

    There has been a great deal of interest lately in studying rings in which every element can be written as a sum of potent elements and nilpotent elements. In this paper, we focus primarily on rings in which every element can be written as the sum of some number of m-potent elements and a nilpotent (for some choice of m), all of which commute with each other. The research that has been conducted thus far in this area has revealed a number of interesting results and intriguing patterns. Our goal in this paper is to unify and extend these results, for the purpose of organizing the current knowledge and facilitating future research in this area.

    Communicated by S. R. López-Permouth

    AMSC: 16U40