Finite Gröbner basis algebras with unsolvable nilpotency problem and zero divisors problem

Ilya Ivanov-Pogodaev, Sergey Malev

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

This work presents a sample construction 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.

Original languageEnglish
Pages (from-to)575-588
Number of pages14
JournalJournal of Algebra
Volume508
DOIs
StatePublished - 15 Aug 2018
Externally publishedYes

Keywords

  • Algorithmic unsolvability
  • Finitely presented algebras
  • Finitely presented rings
  • Finitely presented semigroups
  • Noncommutative Gröbner basis
  • Turing machine

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