Strong and weak F -regularity are equivalent for graded rings
Copyright policy )Strong and weak F -regularity are equivalent for graded rings
It is shown that the tight closure of a submodule in a Artinian module is the same as its finitistic tight closure, when the modules are graded over a finitely generated [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-graded ring over a perfect field. As a corollary, it is deduced that for such a graded ring, strong and weak F -regularity are equivalent. As another application, the following conjecture of Hochster and Huneke is proved: Let ( R, m ) be a finitely generated [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]-graded ring over a field with unique homogeneous maximal ideal m , then R is (weakly) F -regular if and only if R m is (weakly) F -regular.
- University of Minnesota System United States
- University of Michigan–Ann Arbor United States
- University of Minnesota United States
finitistic tight closure, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, F-regularity, Artinian graded module, Frobenius, Commutative Artinian rings and modules, finite-dimensional algebras, Integral closure of commutative rings and ideals, Graded rings, injective hull
finitistic tight closure, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, F-regularity, Artinian graded module, Frobenius, Commutative Artinian rings and modules, finite-dimensional algebras, Integral closure of commutative rings and ideals, Graded rings, injective hull
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