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Tight Closure of Finite Length Modules in Graded Rings
We look at how the equivalence of tight closure and plus closure (or
Frobenius closure) in the homogeneous m-coprimary case implies the same closure
equivalence in the non-homogeneous m-coprimary case in standard graded rings.
Although our result does not depend upon dimension, the primary application is
based on results known in dimension 2 due to the recent results of H. Brenner.
We also show that unlike the Noetherian case, the injective hull of the residue
field over or contains elements that are not killed by any
power of the maximal ideal of R.Comment: 14 pages, minor revisions mad
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