M-Solid Varieties of Algebras provides a complete and systematic
introduction to the fundamentals of the hyperequational theory of
universal algebra, offering the newest results on M-solid varieties
of semirings and semigroups. The book aims to develop the theory of
M-solid varieties as a system of mathematical discourse that is
applicable in several concrete situations. It applies the general
theory to two classes of algebraic structures, semigroups and
semirings. Both these varieties and their subvarieties play an
important role in computer science.
A unique feature of this book is the use of Galois connections
to integrate different topics. Galois connections form the abstract
framework not only for classical and modern Galois theory,
involving groups, fields and rings, but also for many other
algebraic, topological, ordertheoretical, categorical and logical
theories. This concept is used throughout the whole book, along
with the related topics of closure operators, complete lattices,
Galois closed subrelations and conjugate pairs of completely
additive closure operators.
General
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