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# A Gorenstein Ring with Larger Dilworth Number than Sperner Number

Published:2000-03-01
Printed: Mar 2000
• James S. Okon
• J. Paul Vicknair
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## Abstract

A counterexample is given to a conjecture of Ikeda by finding a class of Gorenstein rings of embedding dimension $3$ with larger Dilworth number than Sperner number. The Dilworth number of $A[Z/pZ\oplus Z/pZ]$ is computed when $A$ is an unramified principal Artin local ring.
 MSC Classifications: 13E15 - Rings and modules of finite generation or presentation; number of generators 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings

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