Finite Gröbner basis algebra with unsolvable nilpotency problem and zero divisors problem
I. A. Ivanov-Pogodaev, Sergey Malev · arXiv (Cornell University) · 2016
This work presents a sample constructions of two algebras both with the ideal of relations defined by a finite Gröbner 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.