This book provides an organized exposition of the current state of
the theory of commutative semigroup cohomology, a theory which was
originated by the author and has matured in the past few years. The
work contains a fundamental scientific study of questions in the
theory. The various approaches to commutative semigroup cohomology
are compared. The problems arising from definitions in higher
dimensions are addressed. Computational methods are reviewed. The
main application is the computation of extensions of commutative
semigroups and their classification. Previously the components of
the theory were scattered among a number of research articles. This
work combines all parts conveniently in one volume. It will be a
valuable resource for future students of and researchers in
commutative semigroup cohomology and related areas.
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