Topological representations of distributive lattices and Brouwerian logics
Marshall Harvey Stone (1938)
Časopis pro pěstování matematiky a fysiky
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Topological representations of distributive lattices and Brouwerian logics
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A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.
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We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.