TY - JOUR
T1 - A note on the Buchsbaum-Rim multiplicity of a parameter module
AU - Hayasaka, Futoshi
AU - Hyry, Eero
PY - 2010/2
Y1 - 2010/2
N2 - In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=Ar is bounded above by the colength ℓA(F/N). Moreover, we prove that once the equality ℓA(F/N) = e(F/N) holds true for some parameter module N in F,then the base ring A is Cohen-Macaulay.
AB - In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=Ar is bounded above by the colength ℓA(F/N). Moreover, we prove that once the equality ℓA(F/N) = e(F/N) holds true for some parameter module N in F,then the base ring A is Cohen-Macaulay.
KW - Buchsbaum-Rim multiplicity
KW - Euler-Poincaréchar- acteristic
KW - Generalized Koszul complex
KW - Parameter module
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U2 - 10.1090/S0002-9939-09-10119-3
DO - 10.1090/S0002-9939-09-10119-3
M3 - Article
AN - SCOPUS:77951443869
SN - 0002-9939
VL - 138
SP - 545
EP - 551
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -