On two classes of hereditarily finitely based semigroup identities.
On two papers of B.M. Schein.
On two problems related to cancellativity.
On uniform dimensions of finite groups
Let G be any finite group and L(G) the lattice of all subgroups of G. If L(G) is strongly balanced (globally permutable) then we observe that the uniform dimension and the strong uniform dimension of L(G) are well defined, and we show how to calculate these dimensions.
On uniformly repetitive semigroups.
On unipotent blocks and their ordinary characters.
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 unit group of finite semisimple group algebras of non-metabelian groups up to order 72
We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
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 universal theories of metabelian groups and the Shmel'kin embedding.
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 variants of a theorem of Schur.
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 Hilbert type
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.