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Frobenius test exponents for parameter ideals in generalized Cohen–Macaulay local rings
- Source :
-
Journal of Algebra . Nov2006, Vol. 305 Issue 1, p516-539. 24p. - Publication Year :
- 2006
-
Abstract
- Abstract: This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal of R, there is a power Q of p, depending on , such that the Qth Frobenius power of the Frobenius closure of is equal to the Qth Frobenius power of . The paper addresses the question as to whether there exists a uniform which ‘works’ in this context for all parameter ideals of R simultaneously. In a recent paper, Katzman and Sharp proved that there does exists such a uniform when R is Cohen–Macaulay. The purpose of this paper is to show that such a uniform exists when R is a generalized Cohen–Macaulay local ring. A variety of concepts and techniques from commutative algebra are used, including unconditioned strong d-sequences, cohomological annihilators, modules of generalized fractions, and the Hartshorne–Speiser–Lyubeznik Theorem employed by Katzman and Sharp in the Cohen–Macaulay case. [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*MATHEMATICS
*SCIENCE
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 305
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 22593181
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2006.06.036