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Pseudocomplements in groupoids

Part of: Groupoids

Published online by Cambridge University Press:  09 April 2009

K. Nirmala Kumari Amma
K. Nirmala Kumari Amma
Affiliation:
Department of Mathematics University of Kerala Kariavattom Trivandrum
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Abstract

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This paper is devoted to a study of pseudocomplements in groupoids. A characterization of an intraregular groupoid is obtained in terms of prime ideals. It is proved that the set of dense elements of an intraregular groupoid S with 0 is the intersection of all the maximal filters of S and that the set of normal elements of an intraregular groupoid closed for pseudocomplements forms a Boolean algebra under natural operations. It is shown that the pseudocomplement of an ideal of an intraregular groupoid with 0 is the intersection of all the minimal prime ideas not containing it.

Keywords

Groupoidintraregularsemigrouppseudocomplementnormal elementcutcomplementprime idealfilterBoolean algebra.

MSC classification

Secondary: 20L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 2 , September 1978 , pp. 209 - 219
Copyright
Copyright © Australian Mathematical Society 1978

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