Geodesic
On subalgebra lattices of a finite unary algebra. II
Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 171-181

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We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs $\langle \mathbf{L}_{1},\mathbf{L}_{2}\rangle $ of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to $\mathbf{L}_{1}$ and $\mathbf{L}_{2}$, 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 $\langle \mathbf{L}_{1},\mathbf{L}_{2}, \mathbf{L}_{3},\mathbf{L}_{4}\rangle $ of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to $\mathbf{L}_{1},\mathbf{L}_{2}, \mathbf{L}_{3},\mathbf{L}_{4}$, respectively.
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs $\langle \mathbf{L}_{1},\mathbf{L}_{2}\rangle $ of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to $\mathbf{L}_{1}$ and $\mathbf{L}_{2}$, 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 $\langle \mathbf{L}_{1},\mathbf{L}_{2}, \mathbf{L}_{3},\mathbf{L}_{4}\rangle $ of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to $\mathbf{L}_{1},\mathbf{L}_{2}, \mathbf{L}_{3},\mathbf{L}_{4}$, respectively.
DOI : 10.21136/MB.2001.133927
Classification : 05C20, 05C40, 05C90, 05C99, 06B15, 06D05, 08A30, 08A55, 08A60
Keywords: graph; finite unary algebra; partial algebra; subalgebras; subalgebra lattices 
Pióro, Konrad. On subalgebra lattices of a finite unary algebra. II. Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 171-181. doi: 10.21136/MB.2001.133927
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