Abstract
Many constructions of commutative monoids start with a set P endowed with a partial addition ⊕. The partial structure (P, ⊕) is then extended to a full commutative monoid, which works then as the “enveloping monoid of P”. Although this process has been mostly studied in case P satisfies the refinement axiom (this originates in Tarski [109]), the initial part of the work does not require that axiom.
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Notes
- 1.
The terminology “multiple-free” is borrowed from Tarski [109].
- 2.
Although those modifications might not be, strictly speaking, necessary, I feel that they provide a slightly better presentation than the one of my earlier paper [121], while at the same time gently introducing the reader to those concepts about tensor products of commutative monoids necessary to follow all parts of the present work.
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Wehrung, F. (2017). Partial Commutative Monoids. In: Refinement Monoids, Equidecomposability Types, and Boolean Inverse Semigroups. Lecture Notes in Mathematics, vol 2188. Springer, Cham. https://doi.org/10.1007/978-3-319-61599-8_2
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