TY  - BOOK
AU  - Koppitz,J.
AU  - Denecke,K.
ED  - SpringerLink (Online service)
TI  - M-Solid Varieties of Algebras
T2  - Advances in Mathematics
SN  - 9780387308067
AV  - QA150-272 
U1  - 512 23
PY  - 2006///
CY  - Boston, MA
PB  - Springer US
KW  - Mathematics
KW  - Programming languages (Electronic computers)
KW  - Mathematical logic
KW  - Algebra
KW  - Group theory
KW  - Ordered algebraic structures
KW  - General Algebraic Systems
KW  - Group Theory and Generalizations
KW  - Order, Lattices, Ordered Algebraic Structures
KW  - Programming Languages, Compilers, Interpreters
KW  - Mathematical Logic and Formal Languages
N1  - Basic Concepts -- Closure Operators and Lattices -- M-Hyperidentities and M-solid Varieties -- Hyperidentities and Clone Identities -- Solid Varieties of Arbitrary Type -- Monoids of Hypersubstitutions -- M-Solid Varieties of Semigroups -- M-solid Varieties of Semirings
N2  - 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. Audience This book is intended for researchers in the fields of universal algebra, semigroups, and semirings; researchers in theoretical computer science; and students and lecturers in these fields
UR  - http://dx.doi.org/10.1007/0-387-30806-7
ER  -