A Note on Analytically Irreducible Domains

Roswitha Rissner ()
Additional contact information
Roswitha Rissner: Institute of Analysis and Number Theory

A chapter in Rings, Polynomials, and Modules, 2017, pp 337-352 from Springer

Abstract: Abstract If D is a one-dimensional, Noetherian, local domain, it is well known that D is analytically irreducible if and only if D is unibranched and the integral closure D ′ of D is finitely generated as D-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’s structure theorem for complete, Noetherian, local domains to prove the main result. The purpose of this survey is to make this characterization of analytically irreducible domains more accessible.

Keywords: Unibranched; Analytically irreducible; Noetherian; Local; One-dimensional; 13-02; 13B22, 13B35 13J05, 3J10, 13H05 (search for similar items in EconPapers)
Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_17

Ordering information: This item can be ordered from
http://www.springer.com/9783319658742

DOI: 10.1007/978-3-319-65874-2_17

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().