On the embedding of a commutative ring in a local ring (Q1282991)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the embedding of a commutative ring in a local ring |
scientific article; zbMATH DE number 1274766
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the embedding of a commutative ring in a local ring |
scientific article; zbMATH DE number 1274766 |
Statements
On the embedding of a commutative ring in a local ring (English)
0 references
28 June 1999
0 references
Let \(R\) be a commutative ring with identity. The authors consider conditions in order that there exists an embedding of \(R\) in a local ring. This leads naturally to an examination of conditions in order that a quasilocal ring be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a quasilocal ring. Several results are proved concerning domination of a quasilocal ring by a local ring including the result that a zero-dimensional quasilocal ring that is embeddable in a Noetherian ring is dominated by an Artinian local ring.
0 references
Noetherian ring
0 references
Artinian ring
0 references
local ring
0 references
quasilocal ring
0 references
embedding in a local ring
0 references
extension
0 references
0.9239446
0 references
0.91876775
0 references
0 references
0.91089326
0 references
0.90832436
0 references
0 references
0 references