Rings of Continuous Functions and Totally Integrally Closed Rings

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Noetherian Spaces of Integrally Closed Rings with an Application to Intersections of Valuation Rings

Let H be an integral domain, and let Σ be a collection of integrally closed overrings of H. We show that if A is an overring of H such that H = ( T R∈Σ R)∩A, and if Σ is a Noetherian subspace of the space of all integrally closed overrings of H, then there exists a weakly Noetherian subspace Γ of integrally closed overrings of H such that H = ( T R∈Γ R) ∩ A, and no member of Γ can be omitted fr...

generalized rings of measurable and continuous functions

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Real Closed Rings and Real Closed * Rings

Here we try to distinguish and compare different notions of real closedness mainly one developed by N. Schwartz in his Habilitationschrift and the other developed by A. Sankaran and K. Varadarajan in [SV] which we shall call real closed *. We stick to the definition of real closed rings as defined and characterized in [RCR] and we try to determine and characterize real closed rings that are rea...

Concerning Rings of Continuous Functions