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>