## Algebra II: noncommutative rings, identities, Volume 2This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Comparable in style with Hermann Weyl's evergreen essay The Classical Groups, Shafarevich's new book is sure to become required reading for mathematicians, from beginners to experts. |

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### Contents

Contents | 4 |

FiniteDimensional Algebras | 29 |

Kostrikin I R Shafarevich Steklov Mathematical Institute ul Vavilova | 42 |

Copyright | |

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### Common terms and phrases

A-modules abelian group algebra FG Algebra Logika algebra with identity Artinian ring associative algebra associative rings automorphisms Bakhturin base field basis of identities Brauer group called central simple algebra characteristic zero commutative ring construction contains countable cyclic denote diagram direct sum division ring elements endomorphism English translation equivalent example exists field F field of characteristic finite basis finite group finite-dimensional algebra following theorem free algebra free group Frobenius group algebra group G group varieties homomorphism i?-module idempotents indecomposable infinite injective integer irreducible isomorphic Jacobson radical Krull dimension lattice left ideal Lie algebra linear algebras Mal'tsev mapping Math matrices Mn(F multiplication Neumann nilpotent Noetherian ring non-commutative non-trivial non-zero obtained operation Pi-algebra polynomial prime rings problem Razmyslov regular ring representations result Sect semigroup semiprime semisimple solvable subalgebra submodules subset subvarieties system of identities topological varieties of groups variety 93 vector space zero divisors