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Book review

Author(s) Pinus, A.G.
Title Boolean Constructions in Universal Algebras
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Doina TATAR

This monograph is devoted to studying the fundamentals of the theory of Boolean construction in universal algebras. Chapter 1 is an introduction which presents the basic notions and formulates a number of results of Boolean and universal algebras, many of them published in a monograph by the author: "Congruence-Modular varieties of algebras" (1986). The problem of presenting different varieties of universal algebras are presented in Chapter 2: boolean power, Heyting algebras, Lukasiewicz algebras of the order n, cylindric algebras of dimension n, relation algebras and rings.

The use of Boolean construction for investigating the spectra, skeleton and categories of varieties of universal algebra is presented in Chapter 3.

In the application section (Appendix) one can find the proofs of some statements on Boolean algebras (about well-quasi-ordered set and better-quasi-ordered set) not available in basic monographs on Boolean algebras.

For those who have the good background and interest in Boolean theory this book is a sound investment.