ISSN:
1420-8911
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Stone algebras have been characterized by Chen and Grätzer in terms of triples $ (B, D, \varphi) $ , where D is a distributive lattice with 1, B is a Boolean algebra, and $ \varphi $ is a bounded lattice homomorphism from B into the lattice of filters of D. If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism $ \varphi $ can be replaced by one from B into D itself. The triple construction leads to natural embeddings of a Stone algebra into ones with bounded dense set. These embeddings correspond to a complete sublattice of the distributive lattice of lattice congruences of S. In addition, the largest embedding is a reflector to the subcategory of Stone algebras with bounded dense sets and morphisms preserving the zero of the dense set.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00000326
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