On finitely generated birational flat extensions of integral domains. (English) Zbl 1074.13503

From the introduction: All rings and their extensions are commutative with a unit element. It is well-known that birational, integral, flat extensions of integral domains are trivial.
Our objective is to extend this fact to the result that birational, finitely generated, flat extensions of integral domains are open-immersions. In addition we show that their complementary closed sets are of grade one if not empty.


13G05 Integral domains
13B05 Galois theory and commutative ring extensions
Full Text: DOI Numdam EuDML


[1] Anderson, D. D., A note on minimal prime ideals, Proc. Amer. Math. Soc., 122, 13-14 (1994) · Zbl 0841.13001
[2] Matsumura, H., Commutative Algebra , 2-nd edition (1980) · Zbl 0441.13001
[3] Matsumura, H., Commutative Ring Theory (1986) · Zbl 0603.13001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.