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 $\alpha$-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 $\alpha$-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.PREFACE During the last forty years a new trend in the theory of associative algebras, Lie algebras, and their representations has ... The first class of problems forms a basis of the theory, and it is of interest mainly to specialists in algebra andanbsp;...

Title | : | Identities of Algebras and Their Representations |

Author | : | I͡Uriĭ Pitirimovich Razmyslov |

Publisher | : | American Mathematical Soc. - 1994-01-01 |

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