The Theory of Partial Algebraic Operations / Edition 1

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The main aim of this book is to present a systematic theory of partial groupoids, the so-called pargoids, i.e. systems 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, semi-groups, etc.) and the theory of transformations, but they are connected, and their relations are also studied. This volume will be of interest to researchers of general algebraic systems, group theory, functional analysis and information theory.
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Editorial Reviews

In this updated translation from the original Russian work "Partial Algebraic Operations" (Ljapin & Evseev, Russian State Pedagogical U., St. Petersburg, 1991), a new algebra is introduced that interfaces with the theories of: coding, information, formal languages, the compositions of mappings, and algebraic automata. A theory of partial operations permits the transference to such diverse cases from results of the theory of total operations. Topics span: terminology, initial concepts and properties, homomorphisms, divisibility relations, intermediate associativity, semigroup extensions of partial operations, partial groupoids of transformations, and factorization of partial groupoids. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792346098
  • Publisher: Springer Netherlands
  • Publication date: 6/30/1997
  • Series: Mathematics and Its Applications (closed) Series, #414
  • Edition description: 1997
  • Edition number: 1
  • Pages: 238
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.63 (d)

Table of Contents

Translator's Preface
0 Basic Terminology 1
1 Initial Concepts and Properties 5
2 Homomorphisms 29
3 Divisibility Relations 69
4 Intermediate Associativity 89
5 Semigroup Extensions of Partial Operations 103
6 Partial Groupoids of Transformations 143
7 Factorisation of Partial Groupoids 175
Bibliography 215
Index 233
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