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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Betti numbers of modules of essentially monomial type


Author: Shou-Te Chang
Journal: Proc. Amer. Math. Soc. 128 (2000), 1917-1926
MSC (1991): Primary 13D25, 18G10; Secondary 13H05
Published electronically: February 25, 2000
MathSciNet review: 1653433
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Abstract: Let $R$ be a Noetherian local ring. In this paper we supply formulae for computing the ranks of syzygy and Betti numbers of $R$-modules of essentially monomial type. These modules are defined with respect to various $R$-regular sequences. For example, finite length modules of monomial type over regular local rings of dimension $n$ are modules of essentially monomial type with respect to $R$-regular sequences of length $n$. If a module is of essentially monomial type with respect to an $R$-regular sequence of length $n$, then the rank of its $i$-th syzygy is at least $\binom {n-1}{i-1}$ and its $i$-th Betti number is at least $\binom ni$.


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Additional Information

Shou-Te Chang
Affiliation: Department of Mathematics, National Chung Cheng University, Minghsiung, Chiayi 621, Taiwan, R.O.C.
Email: stchang@math.ccu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05235-7
PII: S 0002-9939(00)05235-7
Received by editor(s): March 24, 1998
Received by editor(s) in revised form: September 1, 1998
Published electronically: February 25, 2000
Additional Notes: The author is partially supported by an N.S.C. grant of R.O.C
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society