Softcover ISBN:  9780821807309 
Product Code:  CBMS/78 
List Price:  $31.00 
Individual Price:  $24.80 
Electronic ISBN:  9781470424381 
Product Code:  CBMS/78.E 
List Price:  $29.00 
Individual Price:  $23.20 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 78; 1991; 55 ppMSC: Primary 16;
The theory of polynomial identities, as a welldefined field of study, began with a wellknown 1948 article of Kaplansky. The field since developed along two branches: the structural, which investigates the properties of rings that satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring that vanish under all specializations in a given ring.
This book is based on lectures delivered during an NSFCBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to \(n\times n\) matrices, including the major structure theorems and the construction of certain polynomial identities and central polynomials for \(n\times n\) matrices. The ring of generic matrices and its center is described. The author then moves on to the invariants of \(n\times n\) matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by \(n\times n\) matrices.
One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of \(n\times n\) matrices. Accessible to those with background at the level of a firstyear graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of problems and research in these areas.Readership 
Table of Contents

Chapters

Polynomial Identity Rings

The Standard Polynomial and the AmitsurLevitzki Theorem

Central Polynomials

Posner’s Theorem and the Ring of Generic Matrices

The Center of the Generic Division Ring

The Capelli Polynomial and Artin’s Theorem

Representation Theory of the Symmetric and General Linear Groups

The First and Second Fundamental Theorems of Matrix Invariants

Applications of the First and Second Fundamental Theorems

The NagataHigman Theorem and Matrix Invariants

Monographs and Survey Articles with Materials on Polynomial Identities


Reviews

This monograph provides an excellent overview of the subject and can serve nonexperts as an introduction to the field and serve experts as a handy reference.
Mathematical Reviews


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The theory of polynomial identities, as a welldefined field of study, began with a wellknown 1948 article of Kaplansky. The field since developed along two branches: the structural, which investigates the properties of rings that satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring that vanish under all specializations in a given ring.
This book is based on lectures delivered during an NSFCBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to \(n\times n\) matrices, including the major structure theorems and the construction of certain polynomial identities and central polynomials for \(n\times n\) matrices. The ring of generic matrices and its center is described. The author then moves on to the invariants of \(n\times n\) matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by \(n\times n\) matrices.
One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of \(n\times n\) matrices. Accessible to those with background at the level of a firstyear graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of problems and research in these areas.

Chapters

Polynomial Identity Rings

The Standard Polynomial and the AmitsurLevitzki Theorem

Central Polynomials

Posner’s Theorem and the Ring of Generic Matrices

The Center of the Generic Division Ring

The Capelli Polynomial and Artin’s Theorem

Representation Theory of the Symmetric and General Linear Groups

The First and Second Fundamental Theorems of Matrix Invariants

Applications of the First and Second Fundamental Theorems

The NagataHigman Theorem and Matrix Invariants

Monographs and Survey Articles with Materials on Polynomial Identities

This monograph provides an excellent overview of the subject and can serve nonexperts as an introduction to the field and serve experts as a handy reference.
Mathematical Reviews