Algebras of Multiplace Functions

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
6.6 Central semigroups of operations
6.7 Algebras of vector-valued functions
6.8 Notes on Chapter 6

7 Open problems
7.1 Closure operations
7.2 Menger algebras of functions
7.3 Menger algebras of relations
7.4 (2, n)-semigroups
7.5 Positional algebras

Bibliography

Index

Wieslaw A. Dudek, Politechnika Wroc?awska, Wroc?aw, Poland; Valentin S. Trokhimenko, Pedagogical University, Vinnitsa, Ukraine.