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The Scientific World Journal
Volume 2014, Article ID 854168, 8 pages
Research Article

The Axioms Independence of Pseudo-Weak- Algebras and Filters

Department of Mathematics and Computer, Wuyi University, Wuyishan, Fujian 354300, China

Received 5 May 2014; Accepted 28 May 2014; Published 7 July 2014

Academic Editor: Hee S. Kim

Copyright © 2014 Yong Lin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The most simplified axiom systems of pseudo-weak- algebras and pseudo- algebras are obtained, and the mutually independence of axioms is proved. We introduce the notions of filters and normal filters in pseudo-weak- algebras. The structures and properties of the generated filters and generated normal filters in pseudo-weak- algebras are obtained. These can be seen as noncommutative generalizations of the corresponding ones in weak- algebras.