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. 
@article{AL_2011_50_4_a1,
     author = {A. V. Zhuchok},
     title = {Dimonoids},
     journal = {Algebra i logika},
     pages = {471--496},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2011_50_4_a1/}
}
TY  - JOUR
AU  - A. V. Zhuchok
TI  - Dimonoids
JO  - Algebra i logika
PY  - 2011
SP  - 471
EP  - 496
VL  - 50
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2011_50_4_a1/
LA  - ru
ID  - AL_2011_50_4_a1
ER  - 
%0 Journal Article
%A A. V. Zhuchok
%T Dimonoids
%J Algebra i logika
%D 2011
%P 471-496
%V 50
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2011_50_4_a1/
%G ru
%F AL_2011_50_4_a1
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/