OHIO UNIVERSITY CENTER FOR
RING THEORY AND ITS APPLICATIONS
LECTURE SERIES
Rings with Polynomial Identities
by
Louis H. Rowen
Bar-Ilan University (ISRAEL)
February 9 - 16, 2006
Lecture I : Rings with Polynomial Identities I (An Overview)
Feb 9th, 2006
1) Definition and some examples
2) Main applications
3) Multilinear and alternating polynomials
4) Identities of matrices
5) Representable algebras
6) Affine algebras
7) The Shirshov program
8) Specht's Conjecture
9) Recent Developments
Lecture II : Rings with Polynomial Identities II
Feb 12th, 2006
We provide new proofs of two of the basic structure theorems of the theory of polynomial identities :
Shirshov's Height theorem (which determines the growth of PI-algebras) and the Razmyslov-Komer-Braun Theoem,
that says the radical of an affine PI-algebra is nilpotent.
Lecture III : Rings with Polynomial Identities III (Specht's Conjecture)
Feb 14th, 2006
We outline Kemer's proof of Specht's conjecture in characteristic 0, that the set of identities of a PI-algebra
is finitely based, and we show how this fails in characteristic p > 0.