Tight closure of powers of ideals and tight hilbert polynomials Article Swipe

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Mathematics Ideal (ethics) Hilbert series and Hilbert polynomial Hilbert–Poincaré series Closure (psychology) Polynomial ring Hypersurface Pure mathematics Combinatorics Polynomial Hilbert's basis theorem Prime (order theory) Ring (chemistry) Hilbert space Mathematical analysis Rigged Hilbert space Reproducing kernel Hilbert space Law Political science Organic chemistry Chemistry

Kriti Goel , J. K. Verma , Vivek Mukundan ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.1017/s0305004119000215 · OA: W2809440569

Let ( R , ) be an analytically unramified local ring of positive prime characteristic p . For an ideal I , let I * denote its tight closure. We introduce the tight Hilbert function $$H_I^*\left( n \right) = \Im \left( {R/\left( {{I^n}} \right)*} \right)$$ and the corresponding tight Hilbert polynomial $$P_I^*\left( n \right)$$ , where I is an m-primary ideal. It is proved that F -rationality can be detected by the vanishing of the first coefficient of $$P_I^*\left( n \right)$$ . We find the tight Hilbert polynomial of certain parameter ideals in hypersurface rings and Stanley-Reisner rings of simplicial complexes.

Tight closure of powers of ideals and tight hilbert polynomials Article Swipe

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