Titlebook: Rings, Polynomials, and Modules; Marco Fontana,Sophie Frisch,Paolo Zanardo Book 2017 Springer International Publishing AG 2017 Gaussian pr

創(chuàng)新

A Note on Analytically Irreducible Domains,ral closure .. of . is finitely generated as .-module. However, the proof of this result is split into pieces and spread over the literature. This paper collects the pieces and assembles them to a complete proof. Next to several results on integral extensions and completions of modules, we use Cohen

Resign

Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions,ars, attention has turned to generalizations of Int(.) where the polynomials act on .-algebras rather than on . itself. We survey the present activity on this topic and propose questions for further research.

GRIN

Unique Factorization in Torsion-Free Modules, In particular, it is shown that locally projective modules, flat Mittag-Leffler modules and torsion-free content modules are factorial modules. Moreover, factorially closed extensions of factorial domains are characterized with help of factorial modules.

舔食

Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat,ring . whose finitely generated ideals are quasi-flat is of .-dimension ≤ 3, and this dimension ≤ 2 if . is local. This extends a former result about the class of arithmetical rings. Moreover, if . has a unique minimal prime ideal, then its finitely generated ideals are quasi-projective if they are quasi-flat.

Assignment

洞穴

誘使

A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative,if (..). = (..). implies ... = ... for every . ∈ x and every ..,?.. ∈ y, then ? is called xy-cancellative. We prove that a gg-cancellative semistar operation on an integral domain need not be gh-cancellative.

雕鏤

,Quasi-Prüfer Extensions of Rings,r extensions that are quasi-Prüfer, the converse being not true. Quasi-Prüfer extensions are closely linked to finiteness properties of fibers. Applications are given for FMC extensions, because they are quasi-Prüfer.

tendinitis

Confidential

Book 2017 also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in boo