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In semigroup theory there are certain kinds of band decompositions, which are useful in the study of the structure semigroups. This book focuses attention on such classes of semigroups and provides a systematic review on this subject. The first chapter is an introduction. The remaining chapters are devoted to special semigroup classes.

Natural duality theory is one of the major growth areas within general algebra. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time.