On Subalgebra Lattices of a Finite Unary Algebra Ii
نویسنده
چکیده
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs 〈L1,L2〉 of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to L1 and L2, 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 〈L1,L2,L3,L4〉 of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to L1,L2,L3,L4, respectively.
منابع مشابه
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 〈A,L〉, where A is a finite unary algebra and L a finite lattice such that the subalgebra lattice of A is isomorphic to L. Moreover, we find necessary and su...
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