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

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...

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Veröffentlicht in:	arXiv.org 2015-07
1. Verfasser:	Stopar, N
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Integrals Mathematical analysis Mathematics - Rings and Algebras Polynomials Rings (mathematics)
Online-Zugang:	Volltext
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