Injective property of generalized inverse polynomial module
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.
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