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Residue Rings of Semi-Primary Hereditary Rings*

Published online by Cambridge University Press:  22 January 2016

Abraham Zaks
Abraham Zaks*
Affiliation:
Brandeis University Waltham, Massachusetts
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Throughout this paper we assume that all rings contain an identity. We say that R is a semi-primary ring if its (Jacobson) radical N is nilpotent, and R/N is an Artinian ring. We say that R admits a splitting, and we write R=A+B if A is a. subring of R, if B is a two-sided ideal in R, and if A∩B=0 .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 279 - 283
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

Footnotes

This paper is based on a part of the author’s doctoral dissertation written at Brandeis University under the direction of Professor Maurice Auslander.

References

[1] Auslander-On, M. the Dimension of Modules and Algebras III, Global Dimension, Nagoya Math, J., 9 (1955), pp. 67–77.Google Scholar
[2] Eilenberg, S., Nagao, H. and Nakoyama-On, T. the Dimension of Modules and Algebras IV, Dimension of Residue Rings of Hereditary Rings, Nagoya Math. J., 10 (1956), pp 87–95 Google Scholar
[3] Jans, J.P. and Nakayama-On, T. the Dimension of Modules and Algebras VIII, Algebras with Finite Dimensional Residue Algebras, Nagoya Math. J., 11 (1957), pp 67–76.Google Scholar
[4] Jacobson-Structure, N. of Rings, Amer. Math. Soc. Col. Pub., vol. 37 (1956).Google Scholar