Algebraic models for accounting systems / Salvador Cruz Rambaud [and others].

Published: Singapore ; Hackensack, N.J. : World Scientific, [2010]
Copyright Date: ©2010
Physical Description: x, 244 pages : illustrations ; 24 cm
Additional Creators: Cruz Rambaud, Salvador

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Contents

Chapter One. Approaches to Accounting Theory -- 1.1. Historical perspectives -- 1.2. Algebraic and proof-based approaches -- 1.3. Natural language approaches -- 1.4. A formal grammar approach -- 1.5. Information systems in information economics -- 1.6. Location of the research justified -- 1.7. Accounting and formal languages -- 1.8. Proof-based systems -- 1.9. The scope of the present work -- Chapter Two. Balance Vectors -- 2.1. The values of an account -- 2.2. The state of an accounting system -- 2.3. Properties of the balance module -- Chapter Three. Transactions -- 3.1. Transaction vectors -- 3.2. Transaction types -- 3.3. Transactions, matrices and digraphs -- Chapter Four. Abstract Accounting Systems -- 4.1. Allowable transactions and balances -- 4.2. Defining an accounting system -- 4.3. Subaccounting systems -- Chapter Five. Quotient Systems and Homomorphisms -- 5.1. Introduction to the quotient concept -- 5.2. Quotients of accounting systems -- 5.3. Homomorphisms of accounting systems -- 5.4. Isomorphism theorems -- Chapter Six. Accounting Systems and Automata -- 6.1. Introduction to semiautomata and automata -- 6.2. Accounting systems as automata I -- 6.3. Accounting systems as automata II -- Chapter Seven. Accounting Systems with Restricted Transactions -- 7.1. An overview of special systems -- 7.2. Finitely specifiable accounting systems -- 7.3. The digraph of a simple system -- Chapter Eight. Algorithms -- 8.1. Decision problems for accounting systems -- 8.2. Recursive accounting systems -- 8.3. The balance verification problem -- 8.4. More algorithms -- Chapter Nine. The Extended Model -- 9.1. Introduction to the 10-tuple model -- 9.2. Authorization and control matrices -- 9.3. Frequency control -- 9.4. The 10-tuple model and automata -- 9.5. The audit as an automaton -- Chapter Ten. The Model Illustrated -- 10.1. A real life example -- 10.2. The operation of the model -- 10.3. Concluding remarks.

Summary

"The book describes the construction of algebraic models which represent the operations of the double entry accounting system. It gives a novel, comprehensive, proof-based treatment of the topic, using such concepts from abstract algebra as automata, digraphs, monoids and quotient structures."--BOOK JACKET.

Subject(s)

Information storage and retrieval systems—Accounting—Mathematical models

ISBN

9789814287111
9814287113

Bibliography Note

Includes bibliographical references and index.

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