A characterization of rings with Krull dimension (Q919078)
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: A characterization of rings with Krull dimension |
scientific article; zbMATH DE number 4158878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of rings with Krull dimension |
scientific article; zbMATH DE number 4158878 |
Statements
A characterization of rings with Krull dimension (English)
0 references
1990
0 references
Many classes of rings can be, and have been, characterized by their cyclic modules. The present authors continue this line of investigation by considering rings with Krull dimension. They consider the following property: (P). Every cyclic right R-module is a direct sum of an injective module and a module containing an essential submodule with Krull dimension at most \(\alpha\). The main result is that a ring with property (P) has right Krull dimension at most \(\alpha\).
0 references
cyclic modules
0 references
Krull dimension
0 references
direct sum
0 references
injective module
0 references
essential submodule
0 references
