Differential operators on Stanley-Reisner rings

Author:
J. R. Tripp

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2507-2523

MSC (1991):
Primary 13N10, 16D25, 16P40

MathSciNet review:
1376559

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Abstract: Let be an algebraically closed field of characteristic zero, and let be a polynomial ring. Suppose that is an ideal in that may be generated by monomials. We investigate the ring of differential operators on the ring , and , the idealiser of in . We show that and are always right Noetherian rings. If is a square-free monomial ideal then we also identify all the two-sided ideals of . To each simplicial complex on there is a corresponding square-free monomial ideal , and the Stanley-Reisner ring associated to is defined to be . We find necessary and sufficient conditions on for to be left Noetherian.

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Additional Information

**J. R. Tripp**

Affiliation:
Pure Math Section, Hicks Building, University of Sheffield, Sheffield S3 7RH, England

Email:
J.R.Tripp@Sheffield.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-97-01749-2

Received by editor(s):
May 9, 1995

Received by editor(s) in revised form:
January 5, 1996

Additional Notes:
I should like to thank Martin Holland for numerous helpful discussions, the referee for constructive comments, and the EPSRC for their funding while this work was completed.

Article copyright:
© Copyright 1997
American Mathematical Society