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 a certain class of monounary algebras
On the lattice of convex subsets of a partial monounary algebra
On weakly rigid monounary algebras