Skip Navigation

Journal of the London Mathematical Society 1984 s2-30(1):15-20; doi:10.1112/jlms/s2-30.1.15
© 1984 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 GOODEARL, K. R.
Right arrow Articles by ROBERTS, P. C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© London Mathematical Society

HEIGHT PLUS DIFFERENTIAL DIMENSION IN COMMUTATIVE NOETHERIAN RINGS

K. R. GOODEARL, T. H. LENAGAN and P. C. ROBERTS

Department of Mathematics, University of Utah Salt Lake City, Utah 84112, U.S.A.

Received 20 June 1983.

Differential dimension and differential codimension for prime ideals in a commutative noetherian ring R equipped with commuting derivations {delta}1,...,{delta}u may be defined in terms of ranks of Jacobian matrices. Given prime ideals P {subseteq} Q in R such that char (R/Q) = 0, it is proved that

diff.codim.(Q)–diff.codim.(P) ≤ ht(Q/P)

and that

ht(P) + diff.dim.(P) ≤ ht(Q) + diff.dim.(Q).

Using the latter inequality, the known formulas for the global dimension and the Krull dimension of the formal differential operator ring R[{theta}1,...,{theta}u] are simplified.

Current address of 2nd author: Department of Mathematics, James Clerk Maxwell Building, The King's Buildings, Edinburgh EH9 3JZ.


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.