Symmetrization of monoïds as hypergroups

Abstract

We adapt the construction of the Grothendieck group associated to a commutative monoïd to handle idempotent monoïds. Our construction works for a restricted class of commutative monoïds, it agrees with the Grothendieck group construction in many cases and yields a hypergroup which solves the universal problem for morphisms to hypergroups. It gives the expected non-trivial hypergroup construction in the case of idempotent monoïds.

7 pages

References in corpus (1)

• Hyperfields for Tropical Geometry I. Hyperfields and dequantization

Cited by in corpus (2)

• Algebraic Geometry Over Hyperrings
• Homology of systemic modules