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 correspondences between relational structures and algebras
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 invariants of unary algebras
On some non-obvious connections between graphs and unary partial algebras
In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras and , their weak subalgebra lattices are isomorphic if and only...
On some non-rational congruences on free commutative semigroups.
On some operator defined on equational classes of algebras
On some properties a projective model class passes on to the generated axiomatic class.
On some properties of genomorphisms of -algebras
On some properties of the family of independent sets in abstract algebras
On some ternary operations in knot theory
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, we obtain the relations from the knot group, and from the core group. Using the ternary operator approach, we generalize the Dehn presentation of the knot group to extra loops, and a similar presentation for the core group to the variety of Moufang loops.
On some unary algebras and their subalgebra lattices
On spectra of solvability and attainability for varieties of semigroups.
On strong regularity of relations
There exists a natural extension of the notion of preorder from binary relations onto relations whose arities are arbitrary ordinals. In the article we find a condition under which extended preorders coincide with preorders if viewed categorically.
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 subdirect decomposition and varieties of some rings with involution. II.