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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Application of the generalized Weierstrass preparation theorem to the study of homogeneous ideals


Author: Mutsumi Amasaki
Journal: Trans. Amer. Math. Soc. 317 (1990), 1-43
MSC: Primary 13A15; Secondary 13C05, 13D25, 13H10, 14M05
DOI: https://doi.org/10.1090/S0002-9947-1990-0992603-9
MathSciNet review: 992603
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Abstract: The system of Weierstrass polynomials, defined originally for ideals in convergent power series rings, together with its sequence of degrees allows us to analyze a homogeneous ideal directly. Making use of it, we study local cohomology modules, syzygies, and then graded Buchsbaum rings. Our results give a formula which to some extent clarifies the connection among the matrices appearing in the free resolution starting from a system of Weierstrass polynomials, a rough classification of graded Buchsbaum rings in the general case and a complete classification of graded Buchsbaum integral domains of codimension two.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0992603-9
Keywords: System of Weierstrass polynomials, Gràbner basis, standard basis, local cohomology, free resolution, Buchsbaum ring
Article copyright: © Copyright 1990 American Mathematical Society