Skip Navigation

Journal of the London Mathematical Society 2000 62(1):41-55; doi:10.1112/S0024610700001010
© 2000 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Viêt Trung, N.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Castelnuovo–Mumford Regularity and Analytic Deviation of Ideals

Ngô Viêt Trung

Institute of Mathematics Box 631, Bò Hô, Hanoi, Vietnam

Received 4 November 1998. Revision received 2 June 1999.

Let (A, m) be a local ring. For convenience we will assume throughout this paper that the residue field of A is infinite.

Let I be an ideal of A. An ideal J {subseteq}I is called a reduction of I if JIn = In+1 for some integer n. The least number n with this property is denoted by rJ (I). A reduction of I is said to be minimal if it does not contain any other reduction of I. The reduction number r(I) of I is the minimum of rJ(I) for all minimal reductions J of I. A minimal reduction of I usually has better properties than I. It can be viewed as an approximation of I and the reduction number is a measure for how it is different from I. The minimal number of generators of every minimal reduction of I is equal to the dimension of the fibre ring {oplus}n≥0In/mIn. This invariant is called the analytic spread of I and denoted by l(I). All these notions have played an important role in ideal theory since their introduction by Northcott and Rees [16].


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.