Bar-Ilan Algebra Seminar ========================================= *** NOTE UNUSUAL TIME *** Date: Wednesday, 3 Adar Sheni 5771 // March 9, 2011 Place: Third floor seminar room, Mathematics building Speaker: Dr. Ilya Ivanov-Pogodaev (Moscow State University) ((10:00 Construction of finitely-presented semigroups with non-integer Gelfand-Kirillov dimension (See separate announcement.))) Time: 11:00 Algebras with finite Grobner basis but algorithmically unsolvable zero-divisors problem Abstract: We construct an algebra $A$ presented by a set of relations with finite Gr\"oebner basis such that the following problems are algorithmically unsolvable. Problem 1. Given an element $a\in A$, does there exist $b\in A$ such that $ab=0$. Problem 2. Given an element $a\in A$, does there exist $n\in N$ such that $a^n=0$. Note that in the case of finite Gr\"oebner basis the equality problem is effectively algorithmically solvable. Note that for finitely presented monomial algebras these problems are algorithmically solvable. The construction is based on the Minsky Machine. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Michael Schein <mschein@math.biu.ac.il>