Regular separably closed rings
It is well known that Pierce's theory of Boolean localization [\textit{R. S. Pierce}, Mem. Am. Math. Soc. 70 (1967; Zbl 0152.026)] is useful in various generalizations of the properties of fields for the case of commutative von Neumann regular rings. The author gives the following interesting example of such a generalization. As it was observed by \textit{Yu. L. Ershov} [Sov. Math., Dokl. 8, 575-576 (1967); translation from Dokl. Akad. Nauk SSSR 174, 19-20 (1967; Zbl 0153.372)], the theories of separable closed fields with certain additional structure are model complete, and replacing the \(\{\) 0,1\(\}\)-valued functional symbols (from this structure) by idempotent-valued (i.e. Boolean-valued) functional symbols, the author obtains model complete theories of ''separably closed regular rings''. As in the case of fields this may be considered as a classification of such theories. The author considers also the connections between separably closed regular rings and differentially closed regular rings.
scientific article; zbMATH DE number 3963998