DECOMPOSITIONS AND EXPANSIONS OF FILTERS IN TARSKI ALGEBRAS

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Published: Nov 15, 2007
DOI: https://doi.org/10.14403/jcms.2007.20.4.457
Keywords:
(quadratic) Tarski algebra, (σ-primary) filter, expansion of filter
Mathematics Subject Classification (2020):
Primary 03B45, 03G25

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Jaedeok Kim
Department of Mathematics, Computing and Information Sciences, Jacksonville State University
Youngmi Kim
Department of Mathematics, Computing and Information Sciences, Jacksonville State University
Eun Hwan Roh
Department of Mathematics Education, Chinju National University of Education

Abstract





We show that any filter of Tarski algebra can be decomposed into the union of some sets. Moreover, we introduce the notion of expansions of filters in Tarski algebras, and discuss the notion of σ-primary filters in Tarski algebras. Finally, we show that there is no non-trivial quadratic Tarski algebras on a field X with |X| ≥ 3.





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Article Details

Issue
Vol. 20 No. 4 (2007)
Section
Articles