Tight closure, plus closure and Frobenius closure in cubical cones |
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Authors: | Moira A. McDermott |
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Affiliation: | Mathematics and Computer Science Department, Gustavus Adolphus College, 800 W. College Avenue, St. Peter, Minnesota 56082-1498 |
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Abstract: | We consider tight closure, plus closure and Frobenius closure in the rings , where is a field of characteristic and . We use a -grading of these rings to reduce questions about ideals in the quotient rings to questions about ideals in the regular ring . We show that Frobenius closure is the same as tight closure in certain classes of ideals when . Since , we conclude that for these ideals. Using injective modules over the ring , the union of all th roots of elements of , we reduce the question of whether for -graded ideals to the case of -graded irreducible modules. We classify the irreducible -primary -graded ideals. We then show that for most irreducible -primary -graded ideals in , where is a field of characteristic and . Hence for these ideals. |
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Keywords: | Tight closure characteristic $p$ Frobenius closure plus closure |
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