Internal monoids and groups in the category of commutative cancellative medial magmas

Pereira Fatelo, Jorge; Martins-Ferreira, Nelson

http://hdl.handle.net/10400.8/13266

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Authors

Pereira Fatelo, Jorge

Martins-Ferreira, Nelson

Abstract(s)

This article considers the category of commutative medial magmas with cancellation, a structure that generalizes midpoint algebras and commutative semigroups with cancellation. In this category each object admits at most one internal monoid structure for any given unit. Conditions for the existence of internal monoids and internal groups, as well as conditions under which an internal reflexive relation is a congruence, are studied.

Keywords

Midpoint algebra Commutative monoid Abelian group Cancellation law Medial law Quasigroup Internal monoid Internal group Internal relation Weakly Mal’tsev category

URI

http://hdl.handle.net/10400.8/13266

Citation

Jorge Pereira Fatelo, Nelson Martins-Ferreira, Internal monoids and groups in the category of commutative cancellative medial magmas. Port. Math. 73 (2016), no. 3, pp. 219–245 DOI 10.4171/PM/1986