Residually FCP extensions of commutative rings

被引：0
|
作者：
Zeidi, Nabil [1 ]
机构：
[1] Sfax Univ, Dept Math, Fac Sci, BP 1171, Sfax 3000, Tunisia
来源：
RICERCHE DI MATEMATICA | 2019年 / 68卷 / 02期
关键词：
Intermediate ring; Minimal ring extension; Maximal chain; FCP and FIP; Finite fibers; INC; 13B02; 13A15; 13B21; 13E05; FIP;
D O I：
10.1007/s11587-018-0409-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A ring extension R subset of S is said to be residually FCP if, for all Q is an element of Spec(S), each chain of rings between R/(QR) and S / Q is finite. The aim of this note is to establish several necessary and sufficient conditions for such extensions. We also study them, with emphasis on base rings R of Krull dimension 0. In particular we show that if R subset of S is residually FCP and dim(R)=0, then S is integral over R. This generalizes a result due to Anderson and Dobbs (Math. Rep. (Bucur.) 3(53):95-103, 2001).
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页码：375 / 381
页数：7
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