Geodesic
Free $n$-dinilpotent doppelsemigroups
Algebra and discrete mathematics, Tome 22 (2016) no. 2, pp. 304-316.

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A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic $K$-theory. In this paper we consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. We construct a free $n$-dinilpotent doppelsemigroup and study separately free $n$-dinilpotent doppelsemigroups of rank $1$. Moreover, we characterize the least $n$-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the free $n$-dinilpotent doppelsemigroup are isomorphic and the automorphism group of the free $n$-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups and prove that a system of axioms of a doppelsemigroup is independent.
Keywords: interassociativity, doppelsemigroup, free $n$-dinilpotent doppelsemigroup, free doppelsemigroup, semigroup, congruence.
Mots-clés : doppelalgebra 
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Anatolii V. Zhuchok; Milan Demko. Free $n$-dinilpotent doppelsemigroups. Algebra and discrete mathematics, Tome 22 (2016) no. 2, pp. 304-316. http://geodesic.mathdoc.fr/item/ADM_2016_22_2_a10/

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