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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Injective compact distributive lattices


Author: Tae Ho Choe
Journal: Proc. Amer. Math. Soc. 37 (1973), 241-245
MSC: Primary 06A35
DOI: https://doi.org/10.1090/S0002-9939-1973-0309818-0
MathSciNet review: 0309818
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Abstract: In the category of zero-dimensional compact distributive lattices and their continuous lattice-homomorphisms, it is firstly shown that the injective objects are precisely the compact Boolean algebras, and each object has an injective envelope. Secondly, it is shown that the category of compact distributive lattices and their continuous lattice-homomorphisms has no non-trivial injective object.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0309818-0
Keywords: Topological lattice, category, injective, injective envelope, power set topological lattice
Article copyright: © Copyright 1973 American Mathematical Society

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