This is a nice introductory course in algebra for undergraduates who may have no previous knowledge of linear algebra. Here is a list of the seventeen chapters of the book: (1) Mappings and operations; (2) Introduction to groups; (3) Equivalence and congruence; (4) Groups; (5) Introduction to rings; (6) The familiar number systems; (7) Group homomorphisms; (8) Applications to permutation groups; (9) Symmetry; (10) Factorization of integers; (11) Polynomials; (12) Quotient rings; (13) Field extensions; (14) Polynomial equations; (15) Geometric constructions; (16) Algebraic coding; (17) Lattices and Boolean algebras. There are four appendices: (A) Sets; (B) Proofs; (C) Mathematical induction; (D) Linear algebra. The author included more than usual on the applications of algebra in his book. There are numerous problems and illustrations. The reviewer's point of view may be somewhat unorthodox, considering the textbooks in algebra available, but he definitely feels there should be some place for semigroups and semilattices, especially since both fields have so many applications. Semigroups and monoids might be introduced just before the groups are considered, and while proving the Cayley representation theorem for groups, the Suškevič representation theorem for semigroups might be proved as a first step. The Cayley theorem follows immediately. Such an arrangement gives the possibility of defining semigroup actions on sets in an exercise (and would prepare students for the later introduction of the concept of a module over a ring). Lattices (and semilattices) have been admitted recently to textbooks, but usually (as in this book) they are considered at the very end, while their proper place is much nearer to the beginning, in which case the author could emphasize lattice-theoretic aspects of various concepts introduced (e.g., lattices of subgroups, etc.).
Reviewer: Schein, Boris M. [form MathSciNet]