Injective property of generalized inverse polynomial module (Q2706504)
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: Injective property of generalized inverse polynomial module |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Injective property of generalized inverse polynomial module |
scientific article |
Statements
19 March 2001
0 references
Noetherian rings
0 references
injective left modules
0 references
inverse polynomial modules
0 references
Injective property of generalized inverse polynomial module (English)
0 references
It has long been known that the module of inverse polynomials \(E[x^{-1}]\) is an injective left \(R[x]\)-module if \(R\) is a left Noetherian ring and \(E\) is an injective left \(R\)-module.NEWLINENEWLINENEWLINEThis note generalizes the above result. Let \(S\) be a submonoid of the set of natural numbers. It is shown that, for \(R\) left Noetherian and \(E\) a left injective \(R\)-module, \(E[x^{-S}]\) is an injective left \(R[x^S]\)-module.
0 references
