3 papers
math.RA2020
Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
Alexei Kanel-Belov, Alexei Chilikov, Ilya Ivanov-Pogodaev +4
This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and…
math.RA2016
A construction of a finitely presented semigroup containing nonnilpotent nil ideal
Ilya Ivanov-Pogodaev, Sergey Malev
This work presents an example of a finitely presented semigroup containing an infinite nonnilpotent nil ideal , whose elements do not have a square (i.e. any word of the ty…
math.RA2016
Finite Gröbner basis algebra with unsolvable nilpotency problem and zero divisors problem
Ilya Ivanov-Pogodaev, Sergey Malev
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 ele…