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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.

MSC:

13G05 Integral domains
13B05 Galois theory and commutative ring extensions
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References:

[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
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