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Quasi-socle ideals in Buchsbaum rings

Published online by Cambridge University Press:  11 January 2016

Shiro Goto ,
Jun Horiuchi  and
Hideto Sakurai
Shiro Goto
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, goto@math.meiji.ac.jp
Jun Horiuchi
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, jhoriuchi@math.meiji.ac.jp
Hideto Sakurai
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, hsakurai@math.meiji.ac.jp
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Abstract

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Quasi-socle ideals, that is, ideals of the form I = Q: mq (q ≥ 2), with Q parameter ideals in a Buchsbaum local ring (A,m), are explored in connection to the question of when I is integral over Q and when the associated graded ring G(I) ⊕ n≥0In/In+1 of I is Buchsbaum. The assertions obtained by Wang in the Cohen-Macaulay case hold true after necessary modifications of the conditions on parameter ideals Q and integers q. Examples are explored.

Keywords

13H1013A3013B2213H15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 200 , December 2010 , pp. 93 - 106
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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