Introduction to abstract algebra. 2nd ed.

*(English)*Zbl 0929.00001
New York, NY: Wiley. xx, 599 p. (1999).

The first edition of the book under review was published in 1993 (Boston: PWS-Kent Publishing Co.) (see the review in Zbl 0781.12001) and this second edition is published almost without any changes. Any abstract algebra book written at undergraduate level for mathematics students has to deal with groups, rings, fields, and Galois theory. Although there is not an independent section on linear algebra in the book the author manages to develop the part of linear algebra which is needed in the proof of well-known theorems. This book is of interest for students outside mathematics as well because it deals with topics such as cryptography, linear codes, cyclic and BCH-codes and combinatorics. The book is well organized into sections and gives the students necessary tools for further study in algebra. A sketch of the history of algebra up to 1929 is included at the beginning of the book.

The content of the book is as follows: 0. Preliminaries 1. Integers and permutations 2. Groups 3. Rings 4. Polynomials 5. Factorization in Integral Domains 6. Fields 7. Finitely Genererated Abelian Groups 8. \(p\)-Groups and the Sylow-Theorems 9. Series of Subgroups 10. Galois Theory 11. Algebras.

The content of the book is as follows: 0. Preliminaries 1. Integers and permutations 2. Groups 3. Rings 4. Polynomials 5. Factorization in Integral Domains 6. Fields 7. Finitely Genererated Abelian Groups 8. \(p\)-Groups and the Sylow-Theorems 9. Series of Subgroups 10. Galois Theory 11. Algebras.

Reviewer: Mohammad-Reza Darafsheh (Tehran)

##### MSC:

00A05 | Mathematics in general |

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 |

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

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

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |