منابع مشابه
Krull Dimension in Modal Logic
We develop the theory of Krull dimension for S4-algebras and Heyting algebras. This leads to the concept of modal Krull dimension for topological spaces. We compare modal Krull dimension to other well-known dimension functions, and show that it can detect differences between topological spaces that Krull dimension is unable to detect. We prove that for a T1-space to have a finite modal Krull di...
متن کاملTopological and Logical Explorations of Krull Dimension
Krull dimension measures the depth of the spectrum Spec(R) of a commutative ring R. Since Spec(R) is a spectral space, Krull dimension can be defined for spectral spaces. Utilizing Stone duality, it can also be defined for distributive lattices. For an arbitrary topological space, the notion of Krull dimension is less useful. Isbell [23] remedied this by introducing the concept of graduated dim...
متن کاملInterval orders and dimension
We show that for every interval order X , there exists an integer t so that if Y is any interval order with dimension at least t, then Y contains a subposet isomorphic to X .
متن کاملDimension de krull des ensembles ordonnes
The notion of deviation of an ordered set has been introduced by Gabriel as a tool to classify rings. It measures how far a given ordered set P deviates from ordered sets satisfying the descending chain condition. We consider here a more general notion and, according to Robson, we define the Krull dimension of P as the deviation of the collection F(P) of its final segments ordered by inclusion....
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.10.005