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Regular closure

Author: Moira A. McDermott
Journal: Proc. Amer. Math. Soc. 127 (1999), 1975-1979
MSC (1991): Primary 13A35, 13H99
Published electronically: March 17, 1999
MathSciNet review: 1487329
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Abstract: Regular closure is an operation performed on submodules of arbitrary modules over a commutative Noetherian ring. The regular closure contains the tight closure when both are defined, but in general, the regular closure is strictly larger. Regular closure is interesting, in part, because it is defined a priori in all characteristics, including mixed characteristic. We show that one can test regular closure in a Noetherian ring $R$ by considering only local maps to regular local rings. In certain cases, it is necessary only to consider maps to certain affine algebras. We also prove the equivalence of two variants of regular closure for a class of rings that includes $R =K[[x,y,z]]/(x^{3}+y^{3}+z^{3})$.

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Additional Information

Moira A. McDermott
Affiliation: Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, Maine 04011-8486
Address at time of publication: Department of Mathematics, Gustavus Adolphus College, 800 West College Avenue, St. Peter, Minnesota 56082

Keywords: Tight closure, regular closure, characteristic $p$
Received by editor(s): August 7, 1997
Received by editor(s) in revised form: October 20, 1997
Published electronically: March 17, 1999
Additional Notes: The author would like to thank the referee for several helpful comments.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society

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