| 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.
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| 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
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| 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 |
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