Separable algebraic closure in a topos

A topos for algebraic quantum theory

ing frames O (X ) coming from a topological space to general frames is a genuine generalization of the concept of a space, as plenty of frames exist tha t are not of the form O (X ). A simple example is the frame Oreg(R) of regular open subsets of R, i.e. of open subsets U with the property ——U = U, where —U is the interior of the complement of U . This may be contrasted with the situation for ...

Algebraic Closure

A Note on Algebraic Closure and Closure under Constraints

A-closure is the equivalent of path consistency for qualitative spatiotemporal calculi with weak composition. We revisit existing attempts to characterize the question whether a-closure is a complete method for deciding consistency of CSPs over such calculi. Renz and Ligozat’s characterization via closure under constraints has been refuted by Westphal, Hué and Wölfl. However, for many commonly ...

Separable integral extensions and plus closure

We show that an excellent local domain of characteristic p has a separable big Cohen–Macaulay algebra. In the course of our work we prove that an element which is in the Frobenius closure of an ideal can be forced into the expansion of the ideal to a module-finite separable extension ring.

A Sheaf Model of the Algebraic Closure

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an alge...