Scalable monoids and quantity calculus

We define scalable monoids and prove their fundamental properties. Congruence relations on scalable monoids, direct and tensor products, subalgebras and homomorphic images of scalable monoids, and unit elements of scalable monoids are defined and investigated. A quantity space is defined as a commut...

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Bibliographic Details
Published in:Semigroup forum 2023-08, Vol.107 (1), p.158-187
Main Author: Jonsson, Dan
Format: Article
Language:English
Subjects:
Algebra
Group theory
Matematik
Mathematical analysis
Mathematical sciences
Mathematics
Mathematics and Statistics
Monoid
Monoids
Quantity calculus
Quantity space
Research Article
Scalable monoid
Tensors
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Summary:We define scalable monoids and prove their fundamental properties. Congruence relations on scalable monoids, direct and tensor products, subalgebras and homomorphic images of scalable monoids, and unit elements of scalable monoids are defined and investigated. A quantity space is defined as a commutative scalable monoid over a field, admitting a finite basis similar to a basis for a free abelian group. Observations relating to the theory of measurement of physical quantities accompany the results about scalable monoids. We conclude that the algebraic theory of scalable monoids and quantity spaces provides a rigorous foundation for quantity calculus.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-023-10371-0