# Seminars 08/09

__Fall 2008 Seminars__

**November 21, 2008**

Adam Van Tuyl (Lakehead University) “Powers of ideals, their associated primes, and connections to graph theory”

**Abstract:**

Let I be an ideal in a ring R. One theme in commutative algebra is to understand the properties of I^s, that is, the s-th power of I, in terms of the properties of the original ideal. In this talk, I will concentrate on the set of associated primes of I^s when I is a monomial ideal constructed from a finite simple graph. I will explain how this set of primes identifies nice subgraphs (odd holes, odd anti-holes, cliques), and how one can use this information to construct an algorithm using algebraic methods to detect perfect graphs.

This is joint work with C. Francisco and T. Ha.

__November 5, 2008__

Yuri Bahturin (MUN), "Jordan gradings on the full matrix algebras"

**Abstract:**

Any associative algebra can be made into a Jordan algebra if we replace the original product xy by a "symmetrized" product xy+yx. In a recent paper with M. Bresar (Slovenia) and I. Shestakov (Brazil) we studied the group gradings of Jordan algebras attached to the associative algebras, for example to the classical matrix algebras. Since the gradings of associative algebras are explored much better, we try to reduce Jordan gradings to the associative ones. This is shown to be possible in a very wide range of cases, thanks to the new techniques coming from the theory of so called functional identities. I plan to briefly explain the results of this theory and to show how they work when applied to the gradings of Jordan algebras.

**October 1, 2008**

Andrew Stewart (MUN) “Gradings on the octonion algebra”

**September 24, 2008**

Yuri Bahturin (MUN) "Generalizations of Schreier Formula. Part 2"

**September 17, 2008**

Yuri Bahturin (MUN) "Generalizations of Schreier Formula."

**Abstract:**

The classical Schreier formula says that if G is a free group with n generators and H a subgroup of index d then the number of generators of equals (n-1)d+1. I will talk about the results of our joint work with Alexander Olshanskii where we expand this formula to the case where the number of generators and/or the index need not be finite. I will also mention relevant results for the free acts over free monoids and free modules over free associative and free group algebras.

__Winter 2009 Seminars__

**February 5, 2009**

Yuri Bahturin (MUN) “Actions of Maximal Growth” (joint work with Alexander Olshanskii, Vanderbilt University)

**Abstract:**

We study acts and modules of maximal growth over finitely generated free monoids and free associative algebras as well as free groups and free group algebras. The maximality of the growth implies some other specific properties of these acts and modules that makes them close to the free ones; at the same time, we show that being a strong "infiniteness" condition, the maximality of the growth can still be combined with various finiteness conditions, which would normally make finitely generated acts finite and finitely generated modules finite-dimensional.

**January 21, 2009**

Matej Bresar (University of Ljubljana and

University of Maribor ) “Functional Identities”