Algebra and Discrete Mathematics, 2010, Vol. 09, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/150362 2026-04-18T13:16:26Z 2026-04-18T13:16:26Z Lattices of classes of groupoids with one-sided quasigroup conditions Galuszka, J. http://dspace.nbuv.gov.ua:80/handle/123456789/154803 2019-06-16T22:30:33Z 2010-01-01T00:00:00Z Lattices of classes of groupoids with one-sided quasigroup conditions Galuszka, J. It is shown that two classes of groupoids satisfying certain one-sided quasigroup conditions, namely the classes of one-sided torsion groupoids and of one-sided finite exponent groupoids, are complete lattices, both isomorphic to the lattice of Steinitz numbers with the divisibility relation. 2010-01-01T00:00:00Z A generalization of groups with many almost normal subgroups Russo, F.G. http://dspace.nbuv.gov.ua:80/handle/123456789/154600 2019-06-15T22:32:15Z 2010-01-01T00:00:00Z A generalization of groups with many almost normal subgroups Russo, F.G. A subgroup H of a group G is called almost normal in G if it has finitely many conjugates in G. A classic result of B. H. Neumann informs us that |G:Z(G)| is finite if and only if each H is almost normal in G. Starting from this result, we investigate the structure of a group in which each non-finitely generated subgroup satisfies a property, which is weaker to be almost normal 2010-01-01T00:00:00Z Length functions for semigroup embeddings Davis, T.C. http://dspace.nbuv.gov.ua:80/handle/123456789/154505 2019-06-15T22:30:54Z 2010-01-01T00:00:00Z Length functions for semigroup embeddings Davis, T.C. Following the work done in [O] for groups, we describe, for a given semigroup S, which functions l:S→N can be realized up to equivalence as length functions g↦|g|H by embedding S into a finitely generated semigroup H. We also, following the work done in [O2] and [OS], provide a complete description of length functions of a given finitely generated semigroup with enumerable set of relations inside a finitely presented semigroup 2010-01-01T00:00:00Z Free commutative dimonoids Zhuchok, A.V. http://dspace.nbuv.gov.ua:80/handle/123456789/154499 2019-06-16T22:30:46Z 2010-01-01T00:00:00Z Free commutative dimonoids Zhuchok, A.V. We construct a free commutative dimonoid and characterize the least idempotent congruence on this dimonoid. 2010-01-01T00:00:00Z