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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 Ilie Parpucea

This book is devoted to studing the fundamentals of the theory of Boolean constructions in universal algebras, to the problems of presenting different varieties of universal algebras with these constructions and to the use of Boolean constructions for investigating the spectra and skeletons of varieties of universal algebras.

Chapter 1 is of an introductory character which presents the basic notions, constructions and results associated with ordered sets and Boolean algebras. The definitions of partially, linearly, well-ordered sets and Boolean algebras, their basic properties, the definitions and properties of the algebraic operations on these sets and algebras can be found in practically any textbook on algebra or set theory.

One of the basic ways the theory of Boolean algebras has been affecting the theory of universal algebras on the whole during the last decades, has been the introduction and wide use of the construction of Boolean powers and their various modifications in universal algebra (chapter 2).

The aim of the chapter 3 is to apply the methods, results and constructions considered in the first two chapters to studies of universal algebra varieties.

The list of references is very rich and adequate. If your personal and/or institutional library is still a bit thin in the important area of universal algebras, this is a volume well worth investing in. There is no index in the book.