Reduction in Rees algebra of modules
\textit{P. Eakin} and \textit{A. Sathaye} [J. Algebra 41, 439--454 (1976; Zbl 0348.13012)] proved that if \(I\) is an ideal in the local ring \(R\) with infinite residue field such that \(I^n\) can be generated by fewer than \(n+r \choose r\) elements, for some integers \(n\geq 1\) and \(r\geq 0\), then there are elements \(y_1,\dots,y_r\) in \(I\), such that \((y_1,\dots, y_r )I^{n-1}=I^n\). In the paper under review, the authors generalize a Eakin-Sathaye theorem for more general class of algebras (Rees Algebras) through application of Zariski open sets associated with the reductions for the Rees algebra of modules.
scientific article; zbMATH DE number 6384238
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