eO-代数簇公理

Axioms in the Variety of {\bf eO}-Algebras

中文关键词:  扩张Ockham代数  对偶空间  次直不可约代数  本原基.

英文关键词:Extended Ockham algebra  dual space  subdirectly irreducible algebra  equational basis.

中文摘要:

      扩张Ockham代数簇$e{\bf O}$是由所有$(L;\wedge,\vee, f, k,0,1)$所组成的代数类,其中$(L;\wedge,\vee,0,1)$是有界分配格, $f$是$L$上的偶同态, $k$是$L$ 是$L$上的同态且满足条件: $fk=kf$. 在本文中,我们把Urquhart定理推广到$e{\bf O}$-代数类,并特别考虑$e{\bf O}$-代数的子代数类 $e_2{\bf M}$.在子代数类$e_2{\bf M}$中, $f$和$k$满足条件: $f^{2}=id_L$及$k^{2}=id_L$. 我们证明: 在子代数类$e_2{\bf M}$中,有19个非等价公理.同时我们给出其蕴含关系的表达图式.

英文摘要:

      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.