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Content and inverse polynomials on Artinian modules. (English) Zbl 0931.13005

Author’s abstract: We investigate when multiplication by a polynomial \(f(X)\) defines a surjective endomorphism on the inverse polynomial module \(M[X^{-1}]\). When \(M\) is Artinian or even a module which has a secondary representation, this is equivalent to \(M=c(f)M\), where \(c(f)\), the content of \(f\), is the ideal generated by the coefficients in \(f\). A criterion for the surjectivity of the endomorphism on \(\text{End}(L,M)\) induced by an endomorphism \(f\) on a finite free module \(L\) is also given.
Reviewer: G.Kowol (Wien)

MSC:

13B25 Polynomials over commutative rings
13E10 Commutative Artinian rings and modules, finite-dimensional algebras
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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References:

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