Journal ArticleDOI
Transfer Results for the FIP and FCP Properties of Ring Extensions
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In this article, the transfer of FCP and FIP properties between E and F is studied for an extension E: R ⊂ S of (commutative) rings and the induced extension F: R(X)⊂ ǫ s of Nagata rings.Abstract:
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.read more
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Some more combinatorics results on Nagata extensions
TL;DR: In this paper, it was shown that the length of ring extensions is preserved under the formation of Nagata extensions as well as Dobbs-Mullins invariant, and a new condition for the FIP property was established by using arithmetic extensions of rings.
Book ChapterDOI
Quasi-Prüfer Extensions of Rings
TL;DR: In this paper, the authors introduce quasi-Prufer ring extensions, which have nice stability properties and are closely linked to finiteness properties of fibers and quasi-prufer rings.
Journal ArticleDOI
Prüfer and Morita Hulls of FCP Extensions
TL;DR: In this article, the authors examine the properties of Morita and Prufer hulls of FCP and FIP extensions of rings and define relative supports that allow direct factorization of an extension and characterize these hulls.
Journal ArticleDOI
When an Extension of Nagata Rings Has Only Finitely Many Intermediate Rings, Each of Those Is a Nagata Ring
TL;DR: Let be an extension of commutative rings, with X an indeterminate, such that the extension of Nagata rings has FIP (i.e., has only finitely many -subalgebras).
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FIP AND FCP products of ring morphisms
TL;DR: In this article, the authors characterize some types of FIP and FCP ring extensions where the ring is a product of rings related to R and also the idealization of an R-module.
References
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Éléments de géométrie algébrique
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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The Theory of Partitions
TL;DR: The generating functions which occur in the theory of partitions and functions closely related to them belong to two important classes of functions, namely the theta functions and the modular functions, both of which have received much attention and have been most thoroughly investigated since the time of Jacobi.
Commutative Algebra I
TL;DR: A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.
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Autour de la platitude
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Lessons on rings, modules and multiplicities
TL;DR: This volume provides a clear and self-contained introduction to important results in the theory of rings and modules and introduces the reader to advanced topics in a manner which makes them both interesting and easy to assimilate.