The Theory of Partial Algebraic Operations

E S Ljapin

ISBN 10: 0792346092 / ISBN 13: 9780792346098

Editore: Springer Jun 1997, 1997

Neuware - Nowadays algebra is understood basically as the general theory of algebraic oper ations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds applica tion at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation. Codice articolo 9780792346098

Riassunto:

The main aim of this volume is to present a systematic theory of partial groupoids, the so-called "paragoids", such as with a single partial binary operation, giving the foundations of this theory, the main problems, and its most important results with full proofs. Attention is paid to specific features of the theory of partial groupoids. This theory is distinct from the theory of total operations (groups and semi-groups) and the theory of transformations, but they are connected, and their relations are also studied. This book should be of interest to researchers of general algebraic systems, group theory, functional analysis and information theory.

Contenuti: Preface. Translator's Preface. 0. Basic Terminology. 1. Initial Concepts and Properties. 2. Homomorphisms. 3. Divisibility Relations. 4. Intermediate Associativity. 5. Semigroup Extensions of Partial Operations. 6. Partial Groupoids of Transformations. 7. Factorisation of Partial Groupoids. Bibliography. Index.

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Titolo: The Theory of Partial Algebraic Operations
Casa editrice: Springer Jun 1997
Data di pubblicazione: 1997
Legatura: Buch
Condizione: Neu