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  • Nilpotent, algebraic and quasi-regular elements in rings and algebras
    Stopar, Nik
    We prove that an integral Jacobson radical ring is always nil, which extends a well-known result from algebras over fields to rings. As a consequence we show that if every element ▫$x$▫ of a ring ... ▫$R$▫ is a zero of some polynomial ▫$p_x$▫ with integer coefficients, such that ▫$p_x(1) = 1$▫, then ▫$R$▫ is a nil ring. With these results we are able to give new characterizations of the upper nilradical of a ring and a new class of rings that satisfy the Köthe conjecture: namely, the integral rings.
    Source: Proceedings of the Edinburgh Mathematical Society. - ISSN 0013-0915 (Vol. 60, part 3, 2017, str. 753-769)
    Type of material - article, component part
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18104921

    Link(s):

    http://doi.org/10.1017/S0013091516000353
    DOI

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