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Nonnoetherian coordinate rings with unique maximal depictions
- Source :
- Communications in Algebra. 46:2635-2647
- Publication Year :
- 2018
- Publisher :
- Informa UK Limited, 2018.
-
Abstract
- A depiction of a nonnoetherian integral domain $R$ is a special coordinate ring that provides a framework for describing the geometry of $R$. We show that if $R$ is noetherian in codimension 1, then $R$ has a unique maximal depiction $T$. In this case, the geometric dimensions of the points of $\operatorname{Spec}R$ may be computed directly from $T$. If in addition $R$ has a normal depiction $S$, then $S$ is the unique maximal depiction of $R$.<br />Comment: 15 pages. To appear, Communications in Algebra
- Subjects :
- Noetherian
Pure mathematics
Algebra and Number Theory
Mathematics::Commutative Algebra
010102 general mathematics
Codimension
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
01 natural sciences
Integral domain
Mathematics - Algebraic Geometry
0103 physical sciences
FOS: Mathematics
Depiction
010307 mathematical physics
0101 mathematics
Affine variety
Algebraic Geometry (math.AG)
Mathematics
Subjects
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 46
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....6c9978dfb1074fdc20db528c74570aa7