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

DOI:
https://doi.org/10.1090/S0002-9939-00-05235-7

Published electronically:
February 25, 2000

MathSciNet review:
1653433

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Noetherian local ring. In this paper we supply formulae for computing the ranks of syzygy and Betti numbers of -modules of essentially monomial type. These modules are defined with respect to various -regular sequences. For example, finite length modules of monomial type over regular local rings of dimension are modules of essentially monomial type with respect to -regular sequences of length . If a module is of essentially monomial type with respect to an -regular sequence of length , then the rank of its -th syzygy is at least and its -th Betti number is at least .

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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:
https://doi.org/10.1090/S0002-9939-00-05235-7

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