By Salvador Cruz Rambaud, José García Pérez, Robert A Nehmer, Derek J S Robinson
This booklet describes the development of algebraic types which characterize the operations of the double access accounting approach. It supplies a singular, complete, evidence established remedy of the subject, utilizing such recommendations from summary algebra as automata, digraphs, monoids and quotient constructions.
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Additional info for Algebraic Models For Accounting Systems
A further phenomenon which occurs when accounting is viewed as a natural language is that the interpretational component becomes closely intertwined with both the syntactic and the semantic components. The conceptual framework and the FASB statements which refine previous interpretations in order to standardize interpretation of economic events indicate the closeness of this relationship. For example, FASB statement number 1 is an attempt to standardize the interpretation of what constitutes an operating lease, as opposed to a capital lease for both the lessee and the lessor.
E(1) = . .. , v is an R-linear combination of e(1), e(2), . . , e(n). If this linear combination equals 0, then the equation shows that v = 0 and so v1 = · · · = vn = 0. Thus the only linear combination of e(1), . . , e(n) that equals 0 is the one with all coefficients equal to 0. This means that e(1), . . , e(n) are linearly independent vectors. As in linear algebra, a subset S of Rn is called an R-basis of Rn if the elements of S are linearly independent and if each vector of R n can be written as a linear combination of vectors in S.
Every transaction is a composite of simple transactions. This means that any transaction, however complex, can be effected by a suitable sequence of exchanges between pairs of accounts. Transactions and T-diagrams In accounting a common way of representing the transactions that have been applied to an accounting system is by means of what are called T-diagrams. Each account has a T-diagram which lists the debits and credits that have been applied to the account in two columns, the column on the left giving the debits and the one on the right the credits.
Algebraic Models For Accounting Systems by Salvador Cruz Rambaud, José García Pérez, Robert A Nehmer, Derek J S Robinson