局部R0-代数

文提出了局部R0-代数的概念,并给出了相应的等价条件,即(i)R0-代数L是局部的,(ii)(?)x∈L,ord(x)<∞或ord(-x)<∞,(iii)每—个真滤子是primary.另外,我们又证明了任一R0-代数是局部R0-代数的子直积.     

Completions of GBL-algebras: negative results

We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang’s chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley. Received August 10, 2006; accepted in final form March 8, 2007.     

低阶MTL-代数

通过数学软件Mathematica得到全部八阶以下的MTL-代数.采用的计算n(n≤8)阶MTL-代数的算法为从低阶有界分配格出发,依据MTL-代数蕴涵算子的特性,借助数学软件找到所有可能的蕴涵运算表;并在此基础上,依据蕴涵算子计算得到相对应的(×)运算表;最后,运用MTL-代数的特征,筛选出所有n阶MTL-代数.     

局部R0-代数

文提出了局部R₀-代数的概念,并给出了相应的等价条件,即(i)R₀-代数L是局部的,(ii) ?x∈L,ord(x)<∞或ord(-x)<∞,(iii)每一个真滤子是primary.另外,我们又证明了任一R₀-代数是局部R₀-代数的子直积.     

Compact representations of BL-algebras

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces. Mathematics Subject Classification (2000):08A72, 03G25, 54B40, 06F99, 06D05