Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-06T18:17:56.755Z Has data issue: false hasContentIssue false
  • English
  • Français

Right Invariant Right Hereditary Rings

Published online by Cambridge University Press:  20 November 2018

H. H. Brungs
H. H. Brungs*
Affiliation:
University of Alberta, Edmonton, Alberta
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1186 - 1191
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Brungs, H. H., Generalized discrete valuation rings, Can. J. Math. 21 (1969), 1404–1408.Google Scholar
2. Brungs, H. H., Filters and overrings (to appear in J. Austral. Math. Soc).Google Scholar
3. Cohn, P. M., Free rings and their relations , London Math. Soc. Monographs No. 2 (Academic Press, New York, 1971).Google Scholar
4. Gilmer, R. W., Multiplicative ideal theory II, Queen's Papers on Pure and Applied Mathematics No. 12 (Queens University, Kingston, Ontario 1968).Google Scholar
5. Jategaonkar, A. V., A counter example in ring theory and homological algebra, J. Algebra 12 (1969), 418–440.Google Scholar
6. Gilmer, R. W., Left principal ideal rings, Lecture Notes in Mathematics No. 123 (Springer Verlag, 1970).Google Scholar
7. Kaplansky, I., Projective modules, Ann. of Math. 68 (1958) 372–377.Google Scholar
8. Lambeck, J., Torsion theories, additive semantics and rings of quotients, Lecture Notes in Mathematics No. 177 (Springer Verlag, 1971).Google Scholar
9. Robson, J. C., Non-commutative Dedekind rings, J. Algebra 9 (1968), 249–265.Google Scholar
10. Robson, J. C. and Eisenbud, D., Modules over Dedekind prime rings, J. Algebra 16 (1970). 67–85.Google Scholar
11. Stenström, B., Rings and modules of quotients, Lecture Notes in Mathematics No. 237 (Springer Verlag, 1971).Google Scholar