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Isometrical Embeddings of Lattices into Geometric Lattices
Order, 2012Embedding lattices into geometric lattices gained substantial interest since the fundamental result of Dilworth on finite lattices. The nice paper under review elaborates on Dilworth's approach and shows that an algebraic lattices endowed with a pseudorank function and having all compact elements of finite height does admit an isometric embedding into ...
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Order, 2013
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Dilip Raghavan, Teruyuki Yorioka
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Dilip Raghavan, Teruyuki Yorioka
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Order, 2007
The author studies lattice-theoretical properties of lattices of uniformities, such as modularity, distributive laws and the existence of (relative) complements. In these investigations the concept of permutable uniformities turns out to be useful: Two uniformities \(u,v\) on a set \(X\) are said to be permutable if \(v\circ u = u\circ v\) where \(u ...
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The author studies lattice-theoretical properties of lattices of uniformities, such as modularity, distributive laws and the existence of (relative) complements. In these investigations the concept of permutable uniformities turns out to be useful: Two uniformities \(u,v\) on a set \(X\) are said to be permutable if \(v\circ u = u\circ v\) where \(u ...
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Journal of Mathematical Imaging and Vision, 2005
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On the sublattice-lattice of a lattice
Algebra Universalis, 1984A property P of algebras in any variety V might be called S-determined if when A has P and A, A' have isomorphic lattices of subalgebras. A' has P; S-sharp if the same conditions imply \(A'=F(A)\) for some automorphism F of V. The authors show that being a pseudocomplemented lattice of finite length is S-determined, and produce two new S-sharp ...
Chen, C.C., Koh, K.M., Teo, K.L.
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On the Congruence Lattice of a Lattice
1990Let L be a lattice. It is proved in N. Funayama and T. Nakayama [10] that the congruence lattice of L is distributive.
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On the sublattice-lattices of lattices
Publicationes Mathematicae Debrecen, 1998For a lattice \(L\), let \(\text{Sub}(L)\) denote the lattice of all sublattices of \(L\), and \(L^d\) the dual of \(L\). If \(L\) and \(K\) are lattices and \(L\approx K\) or \(L\approx K^d\), then \(\text{Sub}(L)\approx \text{Sub}(K)\). The converse in not true in general. The scope of this paper is to prove that if \(L\) and \(K\) are lattices with \
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On congruence lattices of lattices
Algebra Universalis, 1985This paper concerns the old problem, whether every distributive algebraic lattice is isomorphic to the congruence lattice of a lattice. The author discovers a new approach to reduce the representation problem to investigations of congruence lattices of finite lattices. His approach is the following. Let D be the category of finite distributive lattices
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Graphs and Combinatorics, 2002
A pair \((x,y)\) of elements in a lattice is said to be mismatching if \(x\) is join-irreducible, \(y\) is meet-irreducible and \(x\nleqslant y\). The excess of a lattice \(L\) is the number \(\text{ex}(L) =|L|-\min \{|V_x|+ |I_y|\): \((x,y)\) is a mismatching pair\}, where \(V_x\) and \(I_y\) are the filter generated by \(x\) and the ideal generated ...
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A pair \((x,y)\) of elements in a lattice is said to be mismatching if \(x\) is join-irreducible, \(y\) is meet-irreducible and \(x\nleqslant y\). The excess of a lattice \(L\) is the number \(\text{ex}(L) =|L|-\min \{|V_x|+ |I_y|\): \((x,y)\) is a mismatching pair\}, where \(V_x\) and \(I_y\) are the filter generated by \(x\) and the ideal generated ...
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