Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T06:18:02.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Bezout rings and their subrings

Published online by Cambridge University Press:  24 October 2008

P. M. Cohn
P. M. Cohn
Affiliation:
Queen Mary College, London†
Get access Rights & Permissions [Opens in a new window]

Extract

The importance of principal ideal domains (PIDs), both in algebra itself and elsewhere in mathematics is undisputed. By contrast, Bezout rings, ‡ although they represent a natural generalization of PIDs, play a much smaller role and are far less well known. It is true that many of the properties of PIDs are shared by Bezout rings, but the practical value of this observation is questioned by many on the grounds that most of the Bezout rings occuring naturally are in fact PIDs. However, there are several fairly natural methods of constructing Bezout rings from other rings, leading to wide classes of Bezout rings which are not PIDs, and it is the object of this paper to discuss some of these methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 251 - 264
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bourbaki, N.Algèbre, commutative, Ch. 7 (Diviseurs) (Paris, 1965).Google Scholar
(2)Cohn, P. M.Universal Algebra (New York–London–Tokyo, 1965).Google Scholar
(3)Fuchs, L.Riesz groups. Ann. Scuola Norm. Sup. Pisa 19 (1965), 1–34.Google Scholar
(4)Jaffard, P.Les systèmes d'idéaux (Paris, 1960).Google Scholar
(5)Jensen., Chr. U.On characterizations of Prüfer rings. Math. Scand. 13 (1963), 90–98.CrossRefGoogle Scholar
(6)Samuel, P.Anneaux factoriels (São Paulo, 1963).Google Scholar