Basic Notions of Algebra (Encyclopaedia of mathematical sciences ; v. 11) : Basic notions of algebra

Algebra II is a two-part survey on the subject of non-commutative rings and algebras, with the second part focused on the theory of identities of these and other algebraic systems. It provides a broad overview of the most modern trends encountered in non-commutative algebra, as well as the numerous connections between algebraic theories and other areas of mathematics. A wide selection of examples of non-commutative rings is given at the start. Throughout the book, the authors include the historical background of the trends they are discussing. The authors, who are among the most prominent Soviet algebraists, share with their readers their knowledge of the subject, giving them a unique opportunity to learn the material from mathematicians who have made major contributions to it. This is especially true in the case of the theory of identities in varieties of algebraic objects where Soviet mathematicians have been a moving force behind this approach. This monograph on associative rings and algebras, group theory and algebraic geometry is intended for researchers and students.