On totally SLA-simple semigroups
On transformation semigroups which are -semigroups.
On translations in quasidistributive semilattices
On t-semigroups.
On two classes of hereditarily finitely based semigroup identities.
On two papers of B.M. Schein.
On two problems related to cancellativity.
On uniformly repetitive semigroups.
On unique factorization semilattices
The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations...
On universal quasigroup identities
The paper deals with quasigroup identities under isotopies. The terminology is taken from [2], [3] and [4]. Stimulated by geometric illustrations, V. D. Belousov in [2] has presented two important identity properties and posed a question for which identities these properties are necessary and sufficient for the identity to be invariant under isotopies. Inspired by V. D. Belousov, G. Monoszová investigated in [6] one special kind of identities for which both Belousov’s properties give necessary and...
On universality of semigroup varieties
A category is called -determined if every set of non-isomorphic -objects such that their endomorphism monoids are isomorphic has a cardinality less than . A quasivariety is called -universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subquasivarieties of . We say that a variety is var-relatively alg-universal if there exists a proper subvariety of such that homomorphisms of whose image does...
On V n -semigroups
In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups...
On varieties of clones.
On varieties of combinatorial inverse semigroups I.
On varieties of combinatorial inverse semigroups II.
On varieties of completely regular semigroups.
On varieties of completely regular semigroups II.
On varieties of completely regular semigroups III.
On Varieties of Literally Idempotent Languages
A language L ⊆A* is literally idempotent in case that ua2v ∈ L if and only if uav ∈ L, for each u,v ∈ A*, a ∈ A. Varieties of literally idempotent languages result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator on classes of languages. We initiate the systematic study of such varieties. Various classes of literally idempotent languages can be characterized using syntactic methods. A starting example is the...
On varieties of regular -semigroups