Algebras of Multiplace Functions
1st Edition
Published on 4. September 2012
Book
Mixed media product
X, 389 pages
978-3-11-026931-4 (ISBN)
Description
This monograph is devoted to various types of algebras of functions with n variables. It is the first complete monograph (in English) on this topic, covering mainly the Russian literature. It is addressed to all algebraists working in the area of universal algebras, semigroup theory, etc. It is also a useful source of information for graduate and PhD students who are starting their research in this area. The book is the first monograph in the English mathematical literature which provides readers with a very systematical study of the notion of Menger algebras, and its generalizations and applications. The results presented here were originally published mostly in the Russian literature: In 2006, the first version of this book was edited in Russian and it is now presented in an extended version, where two new and very important chapters are added. The monograph is a broad survey of unknown or little-known Russian literature on algebras of multiplace functions and presents to the mathematical community a beautiful and strongly developing theory.
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Wieslaw A. Dudek | Valentin S. Trokhimenko
Algebras of Multiplace Functions
E-Book
08/2012
1st Edition
De Gruyter
€250.00
Available for download
Wieslaw A. Dudek | Valentin S. Trokhimenko
Algebras of Multiplace Functions
Book
08/2012
1st Edition
De Gruyter
€250.00
Shipment within 7-9 days
Persons
Wieslaw A. Dudek, Politechnika Wroclawska, Wroclaw, Poland; Valentin S. Trokhimenko, Pedagogical University, Vinnitsa, Ukraine.
Content
Designations Introduction 1 Main concepts1.1 Elements of the theory of relations1.2 Functions and operations1.3 Algebraic systems1.4 Closure operations1.5 Notes on Chapter 1 2 Menger algebras of functions2.1 Definitions and fundamental notions2.2 Menger semigroups2.3 v-regular Menger algebras2.4 i-solvable Menger algebras2.5 Group-like Menger algebras2.6 Antisymmetric Menger algebras2.7 Representations of Menger algebras2.8 Notes on Chapter 2 3 Ordered Menger algebras3.1 Menger algebras of relations3.2 F.o. and p.q-o. Menger algebras3.3 Algebras of reversive functions3.4 (f)-, (g)-, (f,g)-Menger algebras3.5 Subtraction Menger algebras3.6 Restrictive Menger algebras3.7 Functional Menger systems3.8 Notes on Chapter 3 4 Relations between functions4.1 Stabilizers of Menger algebras4.2 Stabilizers of functional Menger systems4.3 Stationary subsets4.4 Semi-compatibility relation4.5 Co-definability relation4.6 Connectivity relation4.7 Projection equivalence relation4.8 Semiadjacency relation4.9 Notes on Chapter 4 5 (2, n)-semigroups of functions5.1 (2, n)-semigroups and their representations5.2 Menger (2, n)-semigroups5.3 Projection relations on (2, n)-semigroups5.4 Notes on Chapter 5 6 Systems of multiplace functions6.1 Menger systems6.2 Menger T-systems6.3 Positional algebras6.4 Mal'cev-Post iterative algebras6.5 Semigroups of functions6.6 Central semigroups of operations6.7 Algebras of vector-valued functions6.8 Notes on Chapter 6 7 Open problems7.1 Closure operations7.2 Menger algebras of functions7.3 Menger algebras of relations7.4 (2, n)-semigroups7.5 Positional algebras Bibliography Index