Transfer Results for the FIP and FCP Properties of Ring Extensions

Autor:	David E. Dobbs, Martine Picavet-L'Hermitte, Gabriel Picavet
Rok vydání:	2015
Předmět:	Combinatorics Integrally closed Transfer (group theory) Ring (mathematics) Algebra and Number Theory Residue field Support of a module Commutative property Nagata ring Mathematics Antichain
Zdroj:	Communications in Algebra. 43:1279-1316
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927872.2013.856440
Popis:	For an extension E: R ⊂ S of (commutative) rings and the induced extension F: R(X) ⊂ S(X) of Nagata rings, the transfer of the FCP and FIP properties between E and F is studied. Then F has FCP ⇔ E has FCP. The extensions E for which F has FIP are characterized. While E has FIP whenever F has FIP, the converse fails for certain subintegral extensions; it does hold if E is integrally closed, seminormal, or subintegral with R quasi-local having infinite residue field. If F has FIP, conditions are given for the sets of intermediate rings of E and F to be order-isomorphic.
Databáze:	OpenAIRE
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