Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T06:36:07.862Z Has data issue: false hasContentIssue false
  • English
  • Français

Kernel functors for which the associated idempotent kernel functor is stable

Published online by Cambridge University Press:  18 May 2009

J. N. Manocha
J. N. Manocha
Affiliation:
Kent State University, East Liverpool Campus, East Liverpool, Ohio 43920, U.S.A.
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 ring with unity and let denote the category of unital right R-modules. A preradical γ of is a functor γ: → such that

(i) γ(M) ⊆ M for each R-module M,

(ii) for f:M → N, γ(f) is the restriction of f to γ(M).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 103 - 106
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Gabriel, P., Des catégories abeliennes, Bull. Soc. Math. France 90 (1962), 323–448.CrossRefGoogle Scholar
2.Goldman, O., Rings and modules of quotients, J. Algebra 13 (1969), 10–47.CrossRefGoogle Scholar
3.Lambek, J., Torsion theories, additive semantics and rings of quotients, Lecture Notes in Mathematics No. 177 (Springer-Verlag, New York/Berlin, 1971).CrossRefGoogle Scholar
4.Ming, R. Yue Che, A note on singular ideals, Tohoku Math. J. 21 (1969), 337–342.Google Scholar
5.Morita, K., On S-rings, Nagoya Math. J. 27 (1966), 687–695.CrossRefGoogle Scholar
6.Nita, M. C., Sur les anneaux A tells que tout A-module simple est isomorphic à un ideal, C. R. Acad. Paris 268 (1969), 88–91.Google Scholar
7.Stenstrom, B., Rings and modules of quotients, Lecture Notes in Mathematics No. 237 (Springer-Verlag, New York/Berlin, 1971).CrossRefGoogle Scholar