Gauss' lemma and valuation theory. Issue 5 (11th August 2016)
- Record Type:
- Journal Article
- Title:
- Gauss' lemma and valuation theory. Issue 5 (11th August 2016)
- Main Title:
- Gauss' lemma and valuation theory
- Authors:
- Ánh, P.N.
Siddoway, M.F. - Abstract:
- Abstract: Gauss' lemma is not only critically important in showing that polynomial rings over unique factorization domains retain unique factorization; it unifies valuation theory. It figures centrally in Krull's classical construction of valued fields with pre-described value groups, and plays a crucial role in our new short proof of the Ohm-Jaffard-Kaplansky theorem on Bezout domains with given lattice-ordered abelian groups. Furthermore, Eisenstein's criterion on the irreducibility of polynomials as well as Chao's beautiful extension of Eisenstein's criterion over arbitrary domains, in particular over Dedekind domains, are also obvious consequences of Gauss' lemma. We conclude with a new result which provides a Gauss' lemma for Hermite rings.
- Is Part Of:
- Quaestiones mathematicae. Volume 39:Issue 5(2016)
- Journal:
- Quaestiones mathematicae
- Issue:
- Volume 39:Issue 5(2016)
- Issue Display:
- Volume 39, Issue 5 (2016)
- Year:
- 2016
- Volume:
- 39
- Issue:
- 5
- Issue Sort Value:
- 2016-0039-0005-0000
- Page Start:
- 603
- Page End:
- 609
- Publication Date:
- 2016-08-11
- Subjects:
- 13A05 -- 13D05 -- 13F05 -- 06F05
Bezout domains -- Gauss' lemma -- lattice ordered groups
Mathematics -- Periodicals
510.5 - Journal URLs:
- http://www.nisc.co.za/journals?id=7 ↗
http://www.tandfonline.com/loi/tqma20 ↗
http://www.tandfonline.com/ ↗
http://www.ingentaconnect.com/content/nisc/qm? ↗ - DOI:
- 10.2989/16073606.2015.1119214 ↗
- Languages:
- English
- ISSNs:
- 1607-3606
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 7168.117400
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 68.xml