Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Buchsbaum Stanley-Reisner rings with minimal multiplicity


Authors: Naoki Terai and Ken-ichi Yoshida
Journal: Proc. Amer. Math. Soc. 134 (2006), 55-65
MSC (2000): Primary 13F55; Secondary 13D02
DOI: https://doi.org/10.1090/S0002-9939-05-08176-1
Published electronically: August 15, 2005
MathSciNet review: 2170543
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study Buchsbaum Stanley-Reisner rings with linear free resolution. We introduce the notion of Buchsbaum Stanley-Reisner rings with minimal multiplicity of initial degree $q$, which extends the notion of Buchsbaum rings with minimal multiplicity defined by Goto. As an application, we give many examples of non-Cohen-Macaulay Buchsbaum Stanley-Reisner rings with linear resolution.


References [Enhancements On Off] (What's this?)

  • 1. W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge, New York, Sydney, 1993. MR 1251956 (95h:13020)
  • 2. W. Bruns and T. Hibi, Stanley-Reisner rings with pure resolutions, Communications in Algebra 23-4 (1995), 1201-1217. MR 1317395 (96h:13059)
  • 3. J. A. Eagon and V. Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure and Applied Algebra 130 (1998), 265-275. MR 1633767 (99h:13017)
  • 4. D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133. MR 0741934 (85f:13023)
  • 5. R. Fröberg, Rings with monomial relations having linear resolutions, J. Pure Appl. Algebra 38 (1985), 235-241. MR 0814179 (87b:13020)
  • 6. R. Fröberg, On Stanley-Reisner rings, in Topics in algebra,'' Banach Center Publications, No. 26, PWN-Polish Scientific Publishers, Warsaw, 1990, pp. 57-70. MR 1171260 (93f:13009)
  • 7. S. Goto, Buchsbaum rings of maximal embedding dimension, J. Algebra 76 (1982), 383-399. MR 0661862 (83k:13014)
  • 8. S. Goto, On the associated graded rings of parameter ideals in Buchsbaum rings, J. Algebra 85 (1983), 490-534. MR 0725097 (85d:13032)
  • 9. J. Herzog and M. Kühl, On the Betti numbers of finite pure and linear resolutions, Comm. Alg. 22 (1984), 1627-1646. MR 0743307 (85e:13021)
  • 10. T. Hibi, Buchsbaum complexes with linear resolutions, J. Algebra 179 (1996), 127-136. MR 1367844 (97f:13021)
  • 11. L. T. Hoa and C. Miyazaki, Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings, Math. Ann. 301 (1995), 587-598. MR 1324528 (96e:13019)
  • 12. P. Schenzel, Über die freien Auflösungen extremaler Cohen-Macauley-Ringe, J. Algebra 64 (1980), 93-101. MR 0575785 (81j:13024)
  • 13. R. P. Stanley, Combinatorics and Commutative Algebra, Second Edition, Birkhauser, Boston/Basel/Stuttgart, 1996. MR 1453579 (98h:05001)
  • 14. J. Stückrad and W. Vogel, Buchsbaum Rings and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 1986. MR 0881220 (88h:13011a)
  • 15. N. Terai, On h-vectors of Buchsbaum Stanley-Reisner rings, Hokkaido Math. J. 25 (1996), 137-148. MR 1376497 (97b:13028)
  • 16. N. Terai, Alexander duality theorem and Stanley-Reisner ring, in Free resolutions of coordinate rings of projective varieties and related topics (Japanese) (Kyoto, 1998), R.I.M.S. No. 1078 (1999), pp. 174-184. MR 1715588 (2001f:13033)
  • 17. N. Terai, Eisenbud-Goto inequality for Stanley-Reisner rings, Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 379-391, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001. MR 1824243 (2002a:13021)
  • 18. N. Terai and T. Hibi, Computation of Betti numbers of monomial ideals associated with cyclic polytopes, Discrete and Computational Geometry 15 (1996), 287-295. MR 1380395 (96k:13021)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13F55, 13D02

Retrieve articles in all journals with MSC (2000): 13F55, 13D02


Additional Information

Naoki Terai
Affiliation: Department of Mathematics, Faculty of Culture and Education, Saga University, Saga 840–8502, Japan
Email: terai@cc.saga-u.ac.jp

Ken-ichi Yoshida
Affiliation: Graduate School of Mathematics, Nagoya University, Nagoya 464–8602, Japan
Email: yoshida@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-05-08176-1
Keywords: Stanley--Reisner ring, Buchsbaum ring, regularity, linear resolution, Alexander duality, minimal multiplicity
Received by editor(s): August 28, 2004
Published electronically: August 15, 2005
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society