Download PDF by Salvador Cruz Rambaud, José García Pérez, Robert A Nehmer,: Algebraic Models For Accounting Systems

By Salvador Cruz Rambaud, José García Pérez, Robert A Nehmer, Derek J S Robinson

ISBN-10: 9814287113

ISBN-13: 9789814287111

This ebook describes the development of algebraic versions which symbolize the operations of the double access accounting approach. It supplies a unique, finished, facts dependent therapy of the subject, utilizing such options from summary algebra as automata, digraphs, monoids and quotient constructions.

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Under this interpretation, treating the sentence “If the FASB is a governmental agency, then this book is deposited” is equivalent to “either the FASB is not a governmental agency or this book is deposited”, which is true since the FASB is not currently a governmental agency. Notice that the second clause “this book is deposited” can be either true or false and the entire statement remains true as long as the FASB remains independent. As such, the Philonian interpretation of false antecedents is often referred to as the case of trivial truth of the conditional.

Keep in mind that R and R1 are considered to be identical. e. n σ(v) = vi . i=1 It is simple to check that σ has the following properties: σ(v + w) = σ(v) + σ(w), σ(rv) = rσ(v) for all v, w ∈ Rn and r ∈ R. A function between two R-modules with these properties is called an R-module homomorphism. The reason for introducing the function σ is that the vectors v which satisfy σ(v) = 0 are exactly the balance vectors in R n . Now module elements which are sent to zero by a module homomorphism σ form a subset called the kernel , written Ker(σ).

To prove the assertion it is necessary to produce an R-basis consisting of n − 1 vectors. This is done in the next result. 1). Let R be an ordered domain and let n > 1 be an integer. Then the elementary balance vectors e(1, 2), e(2, 3), . . , e(n − 1, n) constitute an R-basis of Baln (R). Thus Baln (R) is a free R-module of rank n − 1. Proof In the first place e(1, 2), . . , e(n − 1, n) are linearly independent. For if r1 , . . , rn−1 ∈ R, then  r1  r2 − r 1     r3 − r 2  , r1 e(1, 2) + r2 e(2, 3) + · · · + rn−1 e(n − 1, n) =  ..

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Algebraic Models For Accounting Systems by Salvador Cruz Rambaud, José García Pérez, Robert A Nehmer, Derek J S Robinson

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