On completions of partial monounary algebras
On congruence lattices of finite partial unary algebras
On congruence relations of monounary algebras. II
On connections between hypergraphs and algebras
The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly, we prove...
On directed convex subsets of partial monounary algebras
On extending of partial Boolean algebras to partial *-algebras
On full partial quasigroups of finite order and local cardinal maximum codes.
On ideal extensions of partial monounary algebras
In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal of a partial monounary algebra we define the quotient partial monounary algebra . Let , be partial monounary algebras. We describe all partial monounary algebras such that is an ideal of and is isomorphic to .
On JP-semilattices of Begum and Noor
In recent papers, S. N. Begum and A. S. A. Noor have studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. We show why their axiom system is too weak to be a satisfactory basis for the authors' constructions and proofs, and suggest an additional axiom for these algebras. We also briefly compare axioms of JP-semilattices with those of nearlattices, another kind of meet semilattices with a partial join...
On one problem in the theory of partial monounary algebras
On quasivarieties of partial algebras, their generation and their subquasivarieties. I
On quasivarieties of partial algebras, their generation and their subquasivarieties II
On some influence of the weak subalgebra lattice on the subalgebra lattice.
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 properties of genomorphisms of -algebras
On some unary algebras and their subalgebra lattices
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 surjective kernels of partial algebras.
On the characterization of primal partial algebras by strong regular hyperidentities.