A survey of modern algebra.
5th ed.

*(English)*Zbl 0863.00001
AKP Classics. Wellesley, MA: A K Peters. xi, 500 p. $59.00, £44.00 (1997).

The first appearance of this book, in the dark days of 1941, was like a breath of fresh air, giving a modern treatment of all the important parts of algebra, including besides the standard topics of groups, rings, fields and vector spaces also linear groups, Boolean algebras and lattices, as well as transfinite arithmetic and some basic algebraic number theory. This mixture, presented with clear proofs and many worked examples, was extremely successful and although slightly modified in successive editions, has kept its appeal; the most notable omission was the subject of categories and functors. The last previous edition, the fourth, appeared in 1977 (see Zbl 0365.00006) with only slight changes.

Now 20 years later, a new publisher has brought out a fifth edition; it differs from the fourth by the correction of some small errors (though the ‘tr(i)angles’ on p. 25 are still i-less). The bibliography is unchanged, apart from listing the new edition of Mac Lane and Birkhoff’s Algebra. 3rd ed. (1988; Zbl 0641.12001). On the whole the text has aged well and it still provides a very readable introduction to the subject, but the price, about which the reviewer in 1977 complained, has almost quadrupled since then.

Now 20 years later, a new publisher has brought out a fifth edition; it differs from the fourth by the correction of some small errors (though the ‘tr(i)angles’ on p. 25 are still i-less). The bibliography is unchanged, apart from listing the new edition of Mac Lane and Birkhoff’s Algebra. 3rd ed. (1988; Zbl 0641.12001). On the whole the text has aged well and it still provides a very readable introduction to the subject, but the price, about which the reviewer in 1977 complained, has almost quadrupled since then.

Reviewer: P.M.Cohn (London)

##### MSC:

00A05 | Mathematics in general |

01A75 | Collected or selected works; reprintings or translations of classics |

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

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

06-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures |

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