ИСТИНА

We discourse some algorithmic problems such that algorithmic undecidability of zero-divisors and nilpotency problem for algebras with finite Groebner basis. Note that for monomial algebras these problems are algorithmically desidable. We also discourse co-growth notion and growth questions of groebner-Shirshov bases in finitely presented algebras. A. Kanel-Belov, I. Melnikov, I Mitrofanov, “On cogrowth function of algebras and its logarithmical gap”, Comptes Rendus - Série Mathématique., 359:3 (2021), 297–303 Ilya Ivanov-Pogodaev, Sergey Malev, “Finite Gröbner basis algebras with unsolvable nilpotency problem and zero divisors problem”, Journal of Algebra, 508 (2018), 575−588