Ring extensions with some finiteness conditions on the set of intermediate rings

Title:

Ring extensions with some finiteness conditions on the set of intermediate rings

Creator:

Jaballah, Ali

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a4142acb-2c36-4d78-80af-af1f5f84f5ed
uuid:a4142acb-2c36-4d78-80af-af1f5f84f5ed

Subject:

integral domain, intermediate ring, overring, integrally closed, Prüfer domain, residually algebraic pair, normal pair, primitive extension, a.c.c., d.c.c., minimal condition, maximal condition, affine extension, Dilworth number, and width of an ordered set

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A ring extension $R\subseteq S$ is said to be FO if it has only finitely many intermediate rings. $R\subseteq S$ is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension $R\subseteq S$ to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair with only finitely many intermediate rings. We also obtain as a corollary several new and old characterizations of Prüfer and integral domains satisfying the corresponding finiteness conditions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

117-124

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:1

Harvested from:

CDK

Metadata only:

false