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Nilpotent, Algebraic and Quasi-Regular Elements in Rings and Algebras

  • Nik Stopar (a1)


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 px with integer coefficients, such that px (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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Nilpotent, Algebraic and Quasi-Regular Elements in Rings and Algebras

  • Nik Stopar (a1)


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