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Some Studies on Semi-local Rings

Published online by Cambridge University Press:  22 January 2016

Masayoshi Nagata
Masayoshi Nagata*
Affiliation:
Mathematical Institute, Nagoya University
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The concept of semi-local rings was introduced by C. Chevalley [1], which the writer has generalized in a recent paper [7] by removing the chain condition. The present paper aims mainly at the study of completions of semi-local rings. First in § 1 we investigate semi-local rings which are subdirect sums of semi-local rings, and we see in § 2 that a Noetherian semi-local ring R is complete if (and only if) R/p is complete for every minimal prime divisor p of zero ideal, together with some other properties. Further we consider in § 3 subrings of the completion of a semi-local ring. § 4 gives some supplementary remarks to [7], Chapter II, Proposition 8.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 3 , October 1951 , pp. 23 - 30
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

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[7] Nagata, M., On the theory of semi-local ring, forthcoming.Google Scholar
[8] Nagata, M., On the theory of radicals in a ring, forthcoming.Google Scholar
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