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arXiv · 1606.01566

Finite Gr\"obner basis algebra with unsolvable nilpotency problem and zero divisors problem

Ilya Ivanov-Pogodaev·Sergey Malev
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Abstract

This work presents a sample constructions of two algebras both with the ideal of relations defined by a finite Gr\"obner basis. For the first algebra the question whether a given element is nilpotent is algorithmically unsolvable, for the second one the question whether a given element is a zero divisor is algorithmically unsolvable. This gives a negative answer to questions raised by Latyshev.

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BibTeXRIS

Ilya Ivanov-Pogodaev, Sergey Malev. 2016-06-05. Finite Gr\"obner basis algebra with unsolvable nilpotency problem and zero divisors problem. https://arxiv.org/abs/1606.01566

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