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The Scientific World Journal
Volume 2014 (2014), Article ID 352381, 8 pages
http://dx.doi.org/10.1155/2014/352381
Research Article

Pseudo-Weak- Algebras

1Department of Mathematics and Computer, Wuyi University, Wuyishan, Fujian 354300, China
2Department of Computer Science and Technology, Chuxiong Normal University, Chuxiong, Yunnan 675000, China

Received 1 March 2014; Revised 7 April 2014; Accepted 10 April 2014; Published 4 May 2014

Academic Editor: Jianming Zhan

Copyright © 2014 Yong Lin Liu and Xiaobo Cai. 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.

Abstract

A positive answer to the open problem of Iorgulescu on extending weak- algebras and -algebras to the noncommutative forms is given. We show that pseudo-weak- algebras are categorically isomorphic to pseudo-IMTL algebras and that pseudo- algebras are categorically isomorphic to pseudo-NM algebras. Some properties, the noncommutative forms of the properties in weak- algebras and -algebras, are investigated. The simplified axiom systems of pseudo-weak- algebras and pseudo- algebras are obtained.