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- Internal monoids and groups in the category of commutative cancellative medial magmasPublication . Pereira Fatelo, Jorge; Martins-Ferreira, NelsonThis 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.
- Reconstructing Classical Algebras via Ternary OperationsPublication . Pereira Fatelo, Jorge; Martins-Ferreira, NelsonAlthough algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified using ternary operations. In this context, we introduce structures that contain two constants and a ternary operation. We demonstrate that these structures are isomorphic to various significant algebraic systems, including Boolean algebras, de Morgan algebras, MV-algebras, and (near-)rings of characteristic two. Our work highlights the versatility of ternary operations in describing and connecting diverse algebraic structures.