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arXiv · 1507.04134

Nilpotent, algebraic and quasi-regular elements in rings and algebras

N. Stopar
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Abstract

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.

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N. Stopar. 2015-07-15. Nilpotent, algebraic and quasi-regular elements in rings and algebras. https://doi.org/10.1017/s0013091516000353

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