Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T00:54:46.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Radical Pairs

Published online by Cambridge University Press:  20 November 2018

N. Divinsky  and
A. Sulinski
N. Divinsky
Affiliation:
University of British Columbia, Vancouver, British Columbia
A. Sulinski
Affiliation:
Warsaw University, Warsaw, Poland
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.

The search for new radicals goes on. Recently R. L. Snider ([6], see page 216) introduced the following notion. Let α and β be any two radicals. A ring R will be said to be an (α : β) ring if for any ideal A of R, we have α (R/A) ≧ β (R/A).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1086 - 1091
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Andrunakievic, W. A., Radicals of assoc. rings I, Matem. Sbornik U (86) (1958), 179–212.Google Scholar
2. Divinsky, N., Rings and radicals (Univ. of Toronto Press, Toronto, 1965).Google Scholar
3. Divinsky, N. Unequivocal rings, Can. J. Math. 27 (1975), 679–690.Google Scholar
4. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970).Google Scholar
5. Procesi, C., Noncommutative Jacobson rings, Ann. Scuola Norm. Sup. Pisa 21 (1967), 281–290.Google Scholar
6. Snider, R. L., Lattices of radicals, Pac. J. Math. 40 (1972), 207–220.Google Scholar
7. Watters, J. F., Polynomial extension of Jacobson rings J. of Algebra 36 (1975), 302–308.Google Scholar
8. Watters, J. F. The Brown-McCoy radical and Jacobson rings, Bull. Acad. Polon. Sci. 24 (1976), 91–100.Google Scholar