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PI-Algebras
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Pi-Algebras
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Free Algebras and PI-algebras
The book is devoted to the combinatorial theory of polynomial algebras, free associative and free Lie algebras, and algebras with polynomial identities. It also examines the structure of automorphism groups of free and relatively free algebras. It is based on graduate courses and short cycles of lectures presented by the author at several universities and its goal is to involve the reader as soon as possible in the research area, to make him or her able to read books and papers on the considered topics. It contains both classical and contemporary results and methods. A specific feature of the book is that it includes as its inseparable part more than 250 exercises and examples with detailed ...
Actions of Linearly Reductive Groups on Affine PI -Algebras
This very interesting monograph straddles two well-studied areas--invariant theory of commutative rings, and the theory of a fixed (noncommutative) ring under a finite group of automorphisms. The author develops a new theory--the fixed subring of a polynomial identity algebra under a linear algebraic group of automorphisms.
Ideals of Identities of Associative Algebras
This book concerns the study of the structure of identities of PI-algebras over a field of characteristic zero. In the first chapter, the author brings out the connection between varieties of algebras and finitely-generated superalgebras. The second chapter examines graded identities of finitely-generated PI-superalgebras. One of the results proved concerns the decomposition of T-ideals, which is very useful for the study of specific varieties. In the fifth section of Chapter Two, the author solves Specht's problem, which asks whether every associative algebra over a field of characteristic zero has a finite basis of identities. The book closes with an application of methods and results established earlier: the author finds asymptotic bases of identities of algebras with unity satisfying all of the identities of the full algebra of matrices of order two.
Identities of Algebras and their Representations
During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.
Algebra
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Computational Aspects of Polynomial Identities
A comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and continuing through the Giambruno-Zaicev exponential rank. T
Selected Papers of S. A. Amitsur with Commentary
The second volume continues--and presumably concludes since they date to two years after his death--the selection of almost all of Amitsur's (1921-1994) work demonstrating his wide and enduring contribution to algebra, though some in Hebrew and some expositions are not included. The sections here are combinatorial polynomial identity theory and division algebras, each introduced by a mathematician. The papers are reproduced from their original publication in a variety of type styles and pay layouts. The biographical sketch must be in the first volume. There is no index. c. Book News Inc.
