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Remarks on affine complete distributive lattices

100%

Zypen D.

Open Mathematics

2006

tom 4

nr 3

525-530

We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.

The subalgebra lattice of a finite algebra

86%

Pióro K.

Open Mathematics

2014

tom 12

nr 7

1052-1108

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.

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2 Open Mathematics

1 Pióro K.

1 Zypen D.

1 2014

1 2006

Wyniki wyszukiwania

Remarks on affine complete distributive lattices

The subalgebra lattice of a finite algebra