Pseudo-algebraically closed rings. (English) Zbl 1018.12008
The author uses a variant of the nonsingular Hasse principle to define a class of rings analogous to pseudo algebraically closed fields and investigates algebraic and model theoretical properties of this class. The paper is a continuation of his earlier work [Nonsingular Hasse principle for rings, J. Reine Angew. Math. 529, 75-100 (2000; Zbl 0959.03021)].
Reviewer: Zbigniew Hajto (Barcelona)
MSC:
12L05 | Decidability and field theory |
12L12 | Model theory of fields |
13L05 | Applications of logic to commutative algebra |
03C60 | Model-theoretic algebra |