q-theory of Finite Semigroups

• I The q operator and Pseudovarieties of Relational Morphisms.- Foundations for Finite Semigroup Theory.- The q-operator.- The Equational Theory.- II Complexity in Finite Semigroup Theory.- The Complexity of Finite Semigroups.- Two-Sided Complexity and the Complexity of Operators.- III The Algebraic Lattice of Semigroup Pseudovarieties.- Algebraic Lattices, Continuous Lattices and Closure Operators.- The Abstract Spectral Theory of PV.- IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product.- Quantales.- The Triangular Product and Decomposition Results for Semirings.

From the book reviews: "The book contains a plethora of exercises, not all routine, open problems and historical and mathematical discussions that are useful for students and researchers ... . This work is a major contribution to the literature in finite semigroup theory and its applications. Both as a reference and as a research monograph pointing to new directions, it should be read in a deep way by anyone interested in this field." (Stuart Margolis, Semigroup Forum, Vol. 89, 2014) "The book presents a new theoretical framework for the study of finite semigroups ... . this monograph will become an important source for people doing relevant research in finite semigroup theory." (K. Auinger, Monatshefte fur Mathematik, Vol. 160 (3), June, 2010) "The book contains a lot of new material on finite semigroup theory. In addition, each chapter of the book ends with ... bibliographic notes. A large number of exercises ... appear throughout the text. ... an extensive bibliography, an index of notation, an author index and an index are also provided. In summary, this book is highly recommended. It provides everyone from graduate students to researchers/practitioners with modern finite semigroup theory at the cutting edge of research." (Francine Blanchet Sadri, Mathematical Reviews, Issue 2010 h) "The book contains an extremely helpful list of frequently used notation; on the web-page of the second author the interested reader will find a q-theory site where new developments and a few errors are documented. The reviewer is quite a bit impressed with this volume and is convinced that this monograph will become an indispensable source and means for everyone who wants to carry out relevant research in finite semigroup theory." (Karl Auinger, Zentralblatt MATH, Vol. 1186, 2010) "This is [a] first-rate presentation of modern finite semigroup theory by two of the currently most active researchers in this field. This is an essential reference for anyone wanting to know the present state-of-the-art in the algebraic theory of semigroups." (Ronald I. Graham, UCSD)