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ON THE CONJECTURE OF VASCONCELOS FOR ARTINIAN ALMOST COMPLETE INTERSECTION MONOMIAL IDEALS

Part of: Local rings and semilocal rings General commutative ring theory Computational aspects and applications Commutative algebra: Homological methods

Published online by Cambridge University Press:  10 December 2019

KUEI-NUAN LIN Open the ORCID record for KUEI-NUAN LIN [Opens in a new window]  and
YI-HUANG SHEN Open the ORCID record for YI-HUANG SHEN [Opens in a new window]
KUEI-NUAN LIN
Affiliation:
Department of Mathematics, The Penn State University, Greater Allegheny Campus, McKeesport, PA, 15132, USA email [email protected]
YI-HUANG SHEN
Affiliation:
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China email [email protected]
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Abstract

In this short note, we confirm a conjecture of Vasconcelos which states that the Rees algebra of any Artinian almost complete intersection monomial ideal is almost Cohen–Macaulay.

MSC classification

Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13D02: Syzygies, resolutions, complexes 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 263 - 277
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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