Abstract algebra.

*(English)*Zbl 0751.00001
Prentice-Hall International Editions. Englewood Cliffs, NJ: Prentice-Hall International, Inc.. xiv, 658 p. (1991).

From the preface: “This book evolved out of notes by the authors from courses given in various universities…The background of students in these courses were quite diverse, ranging from freshman and sophomore undergraduates to beginning graduate students, and included computer science and other science and engineering majors in addition to mathematics majors…We felt that all these students should be given some insight into the main themes in abstract algebra and some understanding of how these themes provide a unifying framework for the study of the basic algebraic structures: groups, rings, fields”.

This is a very carefully written textbook treating the three most important algebra concepts: groups, rings, fields. The group theory is developed as far as to the structure of finitely generated abelian groups, \(p\)-groups, nilpotent groups, solvable groups, and the theory of linear representations of groups. The ring theory includes a standard collection of commutative rings concepts (PID, UFD, rings of fractions etc.) and some basic facts from the module theory. The theory of fields includes the usual portion of Galois theory with the theory of solvable and radical extensions. The book contains a lot of carefully chosen exercises. It is a nice textbook for any interested student though the huge format and the size of book (658 pages) may frighten any person.

This is a very carefully written textbook treating the three most important algebra concepts: groups, rings, fields. The group theory is developed as far as to the structure of finitely generated abelian groups, \(p\)-groups, nilpotent groups, solvable groups, and the theory of linear representations of groups. The ring theory includes a standard collection of commutative rings concepts (PID, UFD, rings of fractions etc.) and some basic facts from the module theory. The theory of fields includes the usual portion of Galois theory with the theory of solvable and radical extensions. The book contains a lot of carefully chosen exercises. It is a nice textbook for any interested student though the huge format and the size of book (658 pages) may frighten any person.

Reviewer: J.Ponizovskij (St.Petersburg)

##### MSC:

00A05 | Mathematics in general |

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

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

15-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra |