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Some Studies on Semi-local Rings
- Source :
- Nagoya Math. J. 3 (1951), 23-30
- Publication Year :
- 1951
- Publisher :
- Cambridge University Press (CUP), 1951.
-
Abstract
- 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 ringRis complete if (and only if)R/pis complete for every minimal prime divisorpof 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.
- Subjects :
- Noetherian
Pure mathematics
Ring (mathematics)
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Local ring
Zero element
Divisor (algebraic geometry)
01 natural sciences
09.1X
Chain (algebraic topology)
0103 physical sciences
0101 mathematics
Minimal prime
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 3
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....9026235509bb3326652b4bd583ba705b