On some algebras connected with the theory of harmony
On some classes of good quotient relations.
On some congruences of power algebras
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class...
On some constructions of algebraic objects
Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.
On some finite groupoids with distributive subgroupoid lattices
The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
On some influence of the weak subalgebra lattice on the subalgebra lattice.
On some non-rational congruences on free commutative semigroups.
On some unary algebras and their subalgebra lattices
On spectra of solvability and attainability for varieties of semigroups.
On subalgebra lattices of a finite unary algebra. I.
One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs , where is a finite unary algebra and a finite lattice such that the subalgebra lattice of is isomorphic to . Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices. We solve...
On subalgebra lattices of a finite unary algebra. II.
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to and , respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples of lattices for which there is a finite unary algebra having...
On subgroupoid lattices of some finite groupoid.
On surjective kernels of partial algebras.
On the approximation of the Boolean powers by Cartesian powers
On the congruence extension property.
On the congruence extension property for compact semigroups.
On the congruence lattice of stable algebras with definability of compact congruences
On the degrees of permutability of subregular varieties
On the existence of non-trivial tolerances in permutable algebras
On the lattice of congruences on inverse semirings
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences and on S and showed that and . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if is a distributive lattice congruence and is a skew-ring congruence on S. If η (σ) is the least distributive...