1. bookVolumen 18 (2018): Heft 4 (August 2018)
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License
Format
Zeitschrift
eISSN
1335-8871
Erstveröffentlichung
07 Mar 2008
Erscheinungsweise
6 Hefte pro Jahr
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Englisch
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The Algebraic Structure of Quantity Calculus

Online veröffentlicht: 14 Aug 2018
Volumen & Heft: Volumen 18 (2018) - Heft 4 (August 2018)
Seitenbereich: 147 - 157
Eingereicht: 19 Jan 2018
Akzeptiert: 15 Jul 2018
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1335-8871
Erstveröffentlichung
07 Mar 2008
Erscheinungsweise
6 Hefte pro Jahr
Sprachen
Englisch
Abstract

The algebraic structure underlying the quantity calculus is defined axiomatically as an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them bound by algebraic restrictions. Subspaces, tensor product, and quotient spaces are considered, as well as homomorphisms to end with a classification theorem of these structures. The new structure provides an axiomatic foundation of quantity calculus which is centered on the concept of dimension, rather than on the concept of unit, which is regarded as secondary, and uses only integer exponents of the dimensions.

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