Higher Cohen-Macaulay property of squarefree modules and simplicial posets
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Abstract:
Recently, G. Fløystad studied higher Cohen-Macaulay property of certain finite regular cell complexes. In this paper, we partially extend his results to squarefree modules, toric face rings, and simplicial posets. For example, we show that if (the corresponding cell complex of) a simplicial poset is $l$-Cohen-Macaulay, then its codimension one skeleton is $(l+1)$-Cohen-Macaulay.References
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Additional Information
- Kohji Yanagawa
- Affiliation: Department of Mathematics, Kansai University, Suita 564-8680, Japan
- Email: yanagawa@ipcku.kansai-u.ac.jp
- Received by editor(s): January 26, 2010
- Received by editor(s) in revised form: August 7, 2010
- Published electronically: January 19, 2011
- Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (c) (no. 19540028).
- Communicated by: Bernd Ulrich
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3057-3066
- MSC (2010): Primary 13F55, 13C14; Secondary 55U10
- DOI: https://doi.org/10.1090/S0002-9939-2011-10734-2
- MathSciNet review: 2811262