Nagoya Mathematical Journal

Quasi-socle ideals in Buchsbaum rings

Shiro Goto, Jun Horiuchi, and Hideto Sakurai

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Quasi-socle ideals, that is, ideals of the form I=Q:mq (q2), 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)=n0In/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.

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Nagoya Math. J., Volume 200 (2010), 93-106.

First available in Project Euclid: 28 December 2010

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Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 13H15: Multiplicity theory and related topics [See also 14C17]


Goto, Shiro; Horiuchi, Jun; Sakurai, Hideto. Quasi-socle ideals in Buchsbaum rings. Nagoya Math. J. 200 (2010), 93--106. doi:10.1215/00277630-2010-013.

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