For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are ...

Let A, B be subgroups of a group G and ∅ 6= X ⊆ G. A subgroup A is said to be X-permutable with B if for some x ∈ X we have ABx = BxA. We obtain some new criterions for supersolubility of a finite group G = AB, where A ...

We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that ...

Dickson characterized groups in terms of one-sided invertibility. In this note, we give comparable characterizations for Bol and Moufang loops.

We consider the dimensions of finite type of rep- resentations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimen- sion. We give a criterion for ...

Let Cay(S, A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S, A) → Cay(S, A) is called an endo-morphism of Cay(S, A) if for each (x, y) ∈ E(Cay(S, ...

We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l > 4 to an equivalent Carter diagram containing only 4-cycles. ...

The Partition algebras Pk(x) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group G called “Extended G-Vertex Colored Partition Algebras," denoted by b Pk(x,G), which contain partition ...