方捷,孙中举.eO-代数簇公理[J].数学研究及应用,2008,28(3):699~705 |
eO-代数簇公理 |
Axioms in the Variety of {\bf eO}-Algebras |
投稿时间:2006-03-01 修订日期:2007-11-22 |
DOI:10.3770/j.issn:1000-341X.2008.03.034 |
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. |
基金项目: |
|
摘要点击次数: 2964 |
全文下载次数: 2153 |
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. |
查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|