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Presentation matrices of torsion modules over polynomial rings. (English) Zbl 1470.13003

This paper deals with presentation matrix of finitely generated modules over \(R[X]\), where \(R\) is a commutative ring. Let \(R\) be a commutative local ring with maximal ideal \(\mathfrak{p}\), \(K\) their residue field and \(M\) be a finitely generated torsion \(R[X]\)-module. The authors describe firstly a basis of \(M\) as \(R\)-module, secondly they give a presentation matrix of the module \(M\) which is square of minimal order of \(M\). This paper concluded by some applications in commutative fields of characteristic \(p>0\).

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
13B10 Morphisms of commutative rings
13C12 Torsion modules and ideals in commutative rings
13E15 Commutative rings and modules of finite generation or presentation; number of generators
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
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