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1999•Taiwanese Journal of MathematicsOpen access

AN ALGORITHM FOR CALCULATING BETTI NUMBERS OF MANAGEABLE MODULES

Shou-Te Chang

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Abstract

In this paper we provide an algorithm for computing Betti numbers and ranks of syzygy of manageable modules with respect to an R-regular sequence of a Noetherian local ring R when certain conditions are met. This method can be applied to many interesting cases and used to verify Horrocks\' conjecture. The problem of calculating Betti numbers is reduced to calculating ranks of certain matrices with a special form over a eld. Our approach is characteristic free.

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In this paper we provide an algorithm for computing Betti numbers and ranks of syzygy of manageable modules with respect to an R-regular sequence of a Noetherian local ring R when certain conditions are met. This method can be applied to many interesting cases and used to verify Horrocks\' conjecture. The problem of calculating Betti numbers is reduced to calculating ranks of certain matrices with a special form over a eld. Our approach is characteristic free.

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Available abstract

In this paper we provide an algorithm for computing Betti numbers and ranks of syzygy of manageable modules with respect to an R-regular sequence of a Noetherian local ring R when certain conditions are met. This method can be applied to many interesting cases and used to verify Horrocks\' conjecture. The problem of calculating Betti numbers is reduced to calculating ranks of certain matrices with a special form over a eld. Our approach is characteristic free.

Key concepts: Hilbert's syzygy theorem, Betti number, Mathematics, Conjecture, Noetherian, Local ring, Algorithm, Sequence (biology)

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