Finite Gr\"obner basis algebra with unsolvable nilpotency problem and zero divisors problem
Rings and Algebras
2017-12-05 v4
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.
Cite
@article{arxiv.1606.01566,
title = {Finite Gr\"obner basis algebra with unsolvable nilpotency problem and zero divisors problem},
author = {Ilya Ivanov-Pogodaev and Sergey Malev},
journal= {arXiv preprint arXiv:1606.01566},
year = {2017}
}