<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

The Algebraic Structure of Quantity Calculus

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The Algebraic Structure of Quantity Calculus"}

The algebraic structure underlying the quantity calculus is defined axiomatically as an algebraic fiber bundle, that is, a base structure which is a free...

The Algebraic Structure of Quantity Calculus

Published Online: Aug 14, 2018

Page range: 147 - 157

Received: Jan 19, 2018

Accepted: Jul 15, 2018

DOI: https://doi.org/10.1515/msr-2017-0021

Keywords
Quantity calculus, algebraic structure, group of dimensions

© 2018 Álvaro P. Raposo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The Algebraic Structure of Quantity Calculus

Published Online: Aug 14, 2018

Page range: 147 - 157

Received: Jan 19, 2018

Accepted: Jul 15, 2018

DOI: https://doi.org/10.1515/msr-2017-0021

KeywordsQuantity calculus, algebraic structure, group of dimensions

© 2018 Álvaro P. Raposo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Quantity calculus, algebraic structure, group of dimensions