Finite Groebner basis algebras with unsolvable nilpotency and zero divisor problems

Wed, 25/01/2017 - 10:30
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Constructions of two algebras, both with the ideal of relations defined by a finite Groebner basis, will be presented. For the first algebra the question of whether a given element is nilpotent is algorithmically unsolvable, for the second the question of whether a given element is a zero divisor is algorithmically unsolvable. This gives a negative answer to questions raised by Latyshev.