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Note on Non-Commutative Semi-Local Rings

Published online by Cambridge University Press:  22 January 2016

Yukitoshi Hinohara
Yukitoshi Hinohara*
Affiliation:
Tokyo Metroporitan University
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Our aim in this note is to generalize some topological results of commutative noetherian rings to non-commutative rings. As a supplemental remark of [2] we prove in § 1 that any right ideal of a complete right semi-local ring is closed, and that

for any finitely generated right module M over a complete right semi-local ring Λ where J is the Jacobson radical of Λ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 17 , August 1960 , pp. 161 - 166
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Akizuki, Y. and Nagata, M., Modern algebra (in Japanese), Ser. of Modern Math., Kyoritsu-Shuppan Co., Tokyo (1957).Google Scholar
[2] Batho, E. H., Non-commutative semi-local and local rings, Duke Math. J., 24 (1957), pp. 163–172.Google Scholar
[3] Cohen, I. S., On the structure and ideal theory of complete local rings, Trans, of the Amer. Math. Soc., 59 (1946), pp. 54–106.CrossRefGoogle Scholar
[4] Cartan, H. and Eilenberg, S., Homological algebra, Princeton Univ., (1956).Google Scholar
[5] Hattori, A., On Prüfer rings, Jour. Math. Soc. Japan, 9 (1957), pp. 381–385.Google Scholar
[6] Hattori, A., A foundation of torsion theory for modules over general rings, Nagoya Math. J., this issue.Google Scholar
[7] Lech, C., Note on multiplicities of ideals, Arkiv for Math., B. 4, H. 1 (1960), pp. 63–86.Google Scholar
[8] Jacobson, N., Structure of rings, Amer. Math. Soc. Colloq. Pub. XXXVII (1956).Google Scholar
[9] Zelinsky, D., Linearly compact modules and rings, Amer. J. of Math., 76 (1953), pp. 79–90.CrossRefGoogle Scholar