Elsevier

Journal of Algebra

Volume 290, Issue 1, 1 August 2005, Pages 250-265
Journal of Algebra

On real closed rings of higher level

https://doi.org/10.1016/j.jalgebra.2005.05.008Get rights and content
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Abstract

The purpose of this paper is to introduce the notion of real closed rings of higher level in the category of reduced commutative rings. Such real closed rings of higher level are just generalized real closed fields in case the rings considered are fields. With the aid of the theory of totally integrally closed rings, some important results on real closed rings of higher level are established. The results in this paper involve real valuations and a related characterization of real closed rings of higher level.

Keywords

Ordering of higher level
Real closed ring of higher level
Real valuation
Tight integral extension
Totally integral closure

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