Axioms in the Variety of {\bf eO}-Algebras |
Received:March 01, 2006 Revised:November 22, 2007 |
Key Words:
Extended Ockham algebra dual space subdirectly irreducible algebra equational basis.
|
Fund Project: |
Author Name | Affiliation | Fang Jie | Department of Mathematics, Shantou University, Guangdong 515063, China Faculty of Mathematics and Computer Science, Guangdong Polytechnic Normal University, Guangdong, 510665, China | SUN Zhong Ju | Department of Mathematics, Shantou University, Guangdong 515063, China |
|
Hits: 2968 |
Download times: 2155 |
Abstract: |
The variety ${\bf eO}$ of extended Ockham algebras consists of those algebras $(L;\wedge, \vee, f$, $k,0,1)$ such that $(L;\wedge,\vee,0,1)$ is a bounded distributive lattice together with a dual endomorphism $f$ on $L$ and an endomorphism $k$ on $L$ such that $fk=kf$. In this paper we extend Urquhart's theorem to ${\bf eO}$-algebras and we are in particular concerned with the subclass ${\bf e_2M}$ of ${\bf eO}$-algebras in which $f^2=id$ and $k^2=id$. We show that there are 19 non-equivalent axioms in ${\bf e_2M}$ and then order them by implication. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2008.03.034 |
View Full Text View/Add Comment |
|
|
|