We introduce the notion of a test exponent for tight closure, and explore its relationship with the problem of showing that tight closure commutes with localization, a longstanding open question. Roughly speaking, test exponents exist if and only if tight closure commutes with localization: mild conditions on the ring are needed to prove this. We give other, independent, conditions that are nec...

A retrospective analysis was performed on forty cases of spinal cord meningiomas, operated on at Dr. Shariati Hospital from 1976 to 1990. Age and sex distribution, clinical presentation and tumor location were comparable to those reported by others. In males the tumors were distributed evenly in cervical and dorsal areas and were often anterior to the cord. This finding makes a different s...

In this article, 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 work of H. Brenner...