Intermediate Rings

Differential Polynomial Rings of Triangular Matrix Rings

On Chains of Intermediate Rings Resulting from the Juxtaposition of Minimal Ring Extensions

Let R ⊂ S and S ⊂ T be minimal ring extensions of (commutative) rings. If (i) each of these extensions is integral or (ii) each of these extensions is integrally closed or (iii) R ⊂ S is integral while S ⊂ T is integrally closed, then each chain of rings between R and T is finite. Examples are given of minimal extensionsR ⊂ S and S ⊂ T such thatR ⊂ S is integrally closed, S ⊂ T is any of the th...

Characterizations of Ideals in Intermediate C-Rings A(X) via the A-Compactifications of X

Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). In Redlin andWatson (1987) and in Panman et al. (2012), correspondencesZ A andZ A are defined between ideals in A(X) and z-filters onX, and it is shown that these extend the well-known correspondences studied separately for C∗(X) andC(X), respectively, to ...

Topology Proceedings 45 (2015) pp. 301-313: Characterizing C(X) among intermediate C-rings on X

Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). We give a characterization of C(X) in terms of extensions of functions in A(X) to real-compactifications of X. We also give equivalences of properties involving the closure in the real-compactifications of X of zero-sets in X; we use these equivalences to ...

Obtaining Intermediate Rings of a Local Profinite Galois Extension without Localization

Let En be the Lubin-Tate spectrum and let Gn be the nth extended Morava stabilizer group. Then there is a discrete Gnspectrum Fn, with LK(n)(Fn) ' En, that has the property that (Fn) ' E n , for every open subgroup U of Gn. In particular, (Fn)n ' LK(n)(S). More generally, for any closed subgroup H of Gn, there is a discrete H-spectrum Zn,H , such that (Zn,H) ' E n . These conclusions are obtain...