Summary and Info
This monograph is the first one in Englishmathematical literature which is devoted to the theory of algebras of functions of several variables. The book contains a comprehensive survey of main topics of this interesting theory. In particular the authors study the notion of Menger algebras and its generalizations in very systematic way. Readers are provided with complete bibliography as well as with systematic proofs of these results. Read more... Designations; Introduction; 1 Main concepts; 1.1 Elements of the theory of relations; 1.2 Functions and operations; 1.3 Algebraic systems; 1.4 Closure operations; 1.5 Notes on Chapter 1; 2 Menger algebras of functions; 2.1 Definitions and fundamental notions; 2.2 Menger semigroups; 2.3 v-regular Menger algebras; 2.4 i-solvable Menger algebras; 2.5 Group-like Menger algebras; 2.6 Antisymmetric Menger algebras; 2.7 Representations of Menger algebras; 2.8 Notes on Chapter 2; 3 Ordered Menger algebras; 3.1 Menger algebras of relations; 3.2 F.o. and p.q-o. Menger algebras; 3.3 Algebras of reversive functions; 3.4 (f)-, (g)-, (f,g)-Menger algebras; 3.5 Subtraction Menger algebras; 3.6 Restrictive Menger algebras; 3.7 Functional Menger systems; 3.8 Notes on Chapter 3; 4 Relations between functions; 4.1 Stabilizers of Menger algebras; 4.2 Stabilizers of functional Menger systems; 4.3 Stationary subsets; 4.4 Semi-compatibility relation; 4.5 Co-definability relation; 4.6 Connectivity relation; 4.7 Projection equivalence relation; 4.8 Semiadjacency relation; 4.9 Notes on Chapter 4; 5 (2, n)-semigroups of functions; 5.1 (2, n)-semigroups and their representations; 5.2 Menger (2, n)-semigroups; 5.3 Projection relations on (2, n)-semigroups; 5.4 Notes on Chapter 5; 6 Systems of multiplace functions; 6.1 Menger systems; 6.2 Menger T-systems; 6.3 Positional algebras; 6.4 Mal'cev-Post iterative algebras; 6.5 Semigroups of functions
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