Bounds for Test Exponents
نویسنده
چکیده
Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that for every ideal I in this class we have that f b ∈ I [p ] if and only if f ∈ I . This gives in particular a finite test for the Frobenius closure. On the other hand we show that there is no uniform bound for Frobenius test exponent for all finitely generated Rmodules N ⊆ M . Under similar assumptions we prove also the existence of a bound for tight closure test ideal exponents for ideals generated by at most n elements. Mathematical Subject Classification (2000): 13A35; 14D20; 14F05; 14H52; 14H60
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