We prove that varieties of abelian dibands and (ln, rn)-dibands coincide, and consider some properties of free abelian dibands.

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 ...

We construct a free product of dimonoids which generalizes a free dimonoid presented by J.-L. Loday and describe its structure.

We describe all semilattice congruences on an arbitrary trioid and define the least semilattice congruence on this trioid. We also show that every trioid is a semilattice of s-simple subtrioids

Доведено, що моноїд ендоморфізмів напіврешітки напівгруп, нерозкладних у напіврешітку, ізоморфно занурюється у вінцевий добуток напівгрупи перетворень з малою категорією.