Two theorems on excellent rings
Two theorems on excellent rings
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优环的两个定理
作者：
S. Greco
令 f: A → B 为交换诺特环的同态。本文的主要结果是： (a) 假设 f 是有限的并在光谱上导出满射映射。那么如果 B 是准优秀的，则 A 是准优秀的，并且如果它是普遍链状的，则 A 是优秀的（Th. 3.1）； (b) 如果 f 绝对平坦且 A 优异，则 B 优异（Th. 5.3）。特别是优秀局部环的严格henselization 非常出色（Cor. 5.6.）。
Let f: A → B be a homomorphism of commutative noetherian rings. The main results of this paper are: (a) Assume f is finite and induces a surjective map on the spectra. Then if B is quasi-excellent A is quasi-excellent and is excellent if it is universally catenarian (Th. 3.1); and (b) If f is absolutely flat and A is excellent then B is excellent (Th. 5.3). In particular the strict henselization of an excellent local ring is excellent (Cor. 5.6.).