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Associated Prime Divisors in the Sense of Krull
- Source :
- Canadian Journal of Mathematics. 24:808-818
- Publication Year :
- 1972
- Publisher :
- Canadian Mathematical Society, 1972.
-
Abstract
- In a recent paper by Douglas Underwood [8] several definitions of “associated prime divisors” were discussed and shown to be unique. In this note we produce a fifth type, which is due to W. Krull, and is found in his classical paper [2] and further discussed by B. Banaschewski in[1].Historically this characterization considerably predates the other four definitions.Throughout this note,Rdenotes a commutative ring with unity, and all ideals and elements are assumed to be in such a ring. We shall let upper case letters, most frequently the beginning of the alphabet, denote ideals and lower case letters, elements ofR.On the whole, our terminology will be that of [9]. We do, however, take exception with [9] in two instances, viz.
- Subjects :
- Ring (mathematics)
General Mathematics
010102 general mathematics
Commutative ring
Regular local ring
Characterization (mathematics)
Type (model theory)
01 natural sciences
Combinatorics
Associated prime
Krull's principal ideal theorem
0103 physical sciences
010307 mathematical physics
Krull dimension
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 24
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........d110154e32a3c0598fa3d47e67dc4d4e