Computational Aspects of Polynomial Identities

Some of the important advances in Polynomial Identity (PI) theory in the last twenty years have remained accessible only to experts, limiting the exposure of advanced aspects of PI-theory to the general mathematical community. This book's main objective is to describe these breakthroughs in full, starting with Shirshov's theorem, discussing Kemer's solution of Specht's conjecture in characteristic zero, and completing with a proof of the theorem. The authors detail the theory needed for this proof in the early chapters of the book. Later chapters discuss related topics such as counterexamples to Specht's conjecture in characteristic p, Noetherian PI-algebras, Poincare-Hilbert series, Gelfand-Kirillov dimension, the combinatoric theory of affine PI-algebras, the ideals of identities, multilinear identities in terms of representation theory, and trace identities.