Zhuchok A. V.
Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1484-1498
We construct a free product of arbitrary n-tuple semigroups, introduce the notion of $n$-band of $n$-tuple semigroups and, in terms of this notion, describe the structure of the free product. We also construct a free commutative $n$-tuple semigroup of an arbitrary rank and characterize one-generated free commutative $n$-tuple semigroups. Moreover, we describe the least commutative congruence on a free $n$-tuple semigroup and establish that the semigroups of the constructed free commutative $n$-tuple semigroup are isomorphic and its automorphism group is isomorphic to the symmetric group.
Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 195–207
We introduce and study the notion of semiretraction of trioid. Examples of left, right, and symmetric semiretractions of trioids are given. We also present new theoretical trioid constructions for which some symmetric semiretractions are characterized.
Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 165-175
We characterize the least semilattice congruence on the free dimonoid and prove that the free dimonoid is a semilattice of s-simple subdimonoids each being a rectangular band of subdimonoids.