Geodesic
Dimonoids
Algebra i logika, Tome 50 (2011) no. 4, pp. 471-496.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a system of axioms for a dimonoid is independent and Cayley's theorem for semigroups has an analog in the class of dimonoids. A least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation. It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. A least separative congruence on a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, and each dimonoid with a commutative operation is a semilattice of $a$-connected subdimonoids. Different dimonoid constructions are presented.
Keywords: dimonoid, dimonoid with commutative operation, free commutative dimonoid, semilattice of subdimonoids, semigroup. 
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A. V. Zhuchok. Dimonoids. Algebra i logika, Tome 50 (2011) no. 4, pp. 471-496. http://geodesic.mathdoc.fr/item/AL_2011_50_4_a1/

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