Algebraically birational extensions (Q1345910)

Birational algebras are generalizations of Zariski central rings. Their definition is purely topological, in terms of open sets in the Zariski topology. The paper adds an algebraic condition (which is intrinsically non-commutative) in order to obtain non-commutative information from central information. The basic tools introduced in this paper lead to what might be called the ideal theory of birational extensions.