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A Gorenstein Ring with Larger Dilworth Number than Sperner Number

Published online by Cambridge University Press:  20 November 2018

James S. Okon  and
J. Paul Vicknair
James S. Okon
Affiliation:
Department of Mathematics California State University San Bernardino, California 92374 U.S.A., email: jokon@csusb.edu
J. Paul Vicknair
Affiliation:
Department of Mathematics California State University San Bernardino, California 92374 U.S.A., email: jvicknai@csusb.edu
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Abstract

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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 $A\left[ {Z}/{pZ}\;\,\oplus \,{Z}/{pZ}\; \right]$ is computed when $A$ is an unramified principal Artin local ring.

Keywords

13E1516S34
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 100 - 104
Copyright
Copyright © Canadian Mathematical Society 2000

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