Abstract
When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.
Original language | English |
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Pages (from-to) | 3686-3698 |
Number of pages | 13 |
Journal | Communications in Algebra |
Volume | 38 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2010 |
Externally published | Yes |
Keywords
- Arithmetical rank
- Monomial ideals
- Projective dimension
- Set-theoretic complete intersections
ASJC Scopus subject areas
- Algebra and Number Theory