Algebra. Volume 2. 2nd ed.

*(English)*Zbl 0703.00002
Chichester etc.: John Wiley & Sons. xv, 428 p. £14.95 (1989).

From the preface to the second edition: “The present volume includes the whole of four chapters from old Vol. 2, about half of another four, while the rest are represented by smaller proportions. The introductory chapters, on sets and lattices, omit the Peano axioms, but sections on graphs and categories have been added. This is followed by a chapter on field theory, covering Galois theory as well as the notion of algebraic closure. Next come modules, rings and algebras; here many examples and constructions are given, but the theory is only taken as far as the Wedderburn theorems and the radical. A chapter on quadratic forms and ordered fields deals with the more elementary parts from the old Vol. 2, while the chapters on valuations and commutative rings are included in their entirety.”

There are also three new chapters: Ch. 7 on representation theory of finite groups; Ch. 10 in which an introduction to block codes is given; Ch. 11 which deals with algebraic language theory and related topics of variable-length codes, automata and power series rings. The present Vol. 2 contains topics for third-year undergraduate courses. The author projects also to prepare Vol. 3 which will be devoted to postgraduate work.

Contents: Sets, Lattices, Field theory, Modules, Rings and algebras, Quadratic forms and ordered fields, Representation theory of finite groups, valuation theory, Commutative rings, Coding theory, Languages and automata.

For reviews of the former editions (London 1974, 1977 and Chichester 1982) see Zbl 0272.00003 (Vol. 1), Zbl 0341.00002 (Vol. 2) and Zbl 0481.00001 (Vol. 1).

There are also three new chapters: Ch. 7 on representation theory of finite groups; Ch. 10 in which an introduction to block codes is given; Ch. 11 which deals with algebraic language theory and related topics of variable-length codes, automata and power series rings. The present Vol. 2 contains topics for third-year undergraduate courses. The author projects also to prepare Vol. 3 which will be devoted to postgraduate work.

Contents: Sets, Lattices, Field theory, Modules, Rings and algebras, Quadratic forms and ordered fields, Representation theory of finite groups, valuation theory, Commutative rings, Coding theory, Languages and automata.

For reviews of the former editions (London 1974, 1977 and Chichester 1982) see Zbl 0272.00003 (Vol. 1), Zbl 0341.00002 (Vol. 2) and Zbl 0481.00001 (Vol. 1).

Reviewer: J.S.Ponizovskij

##### MSC:

00A05 | Mathematics in general |

03-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations |

12-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory |

13-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra |

16-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras |

20-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory |