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Eakin-Sathaye-Type Theorems for Joint Reductions and Good Filtrations of Ideals

Kriti Goel , Sudeshna Roy , $icon-email$ J. K. Verma

Abstract

Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for $N^{s}$ -graded good filtrations. These analogues yield bounds on joint reduction vectors for a family of ideals and reduction numbers for $N$ -graded filtrations. Several examples related to lex-segment ideals, contracted ideals in 2-dimensional regular local rings and the filtration of integral and tight closures of powers of ideals in hypersurface rings are constructed to show effectiveness of these bounds.

Acta Mathematica Vietnamica

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Eakin-Sathaye-Type Theorems for Joint Reductions and Good Filtrations of Ideals

Abstract