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An algebraic structure underlying the quantity calculus is proposedconsisting in an algebraic fiber bundle, that is, a base structure which is afree Abelian group together with fibers which are one dimensional vectorspaces, all of them bound by algebraic restrictions. Subspaces, tensor productand quotient spaces are considered as well as homomorphisms to end with aclassification theorem of these structures. The new structure provides anaxiomatic foundation for quantity calculus and gives complete justificationwithin its framework of the way that quantity calculus is actually performed.It is hoped that this exposition helps to clarify the role of the intervieningconcepts of quantity, quantity value, quantity dimension and their relationwith a system of units, particularly, the SI.

The algebraic structure of quantity calculus