Algebraic Models for Accounting Systems

This book describes the construction of algebraic models which represent the operations of the double-entry accounting system. It presents a novel and comprehensive treatment of the subject and utilizes the methods and tools of abstract algebra, including automata, graph theory and monoids.

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.