金晨辉.并素元有限生成格的弱直积分解[J].数学研究及应用,2000,20(2):283~286
并素元有限生成格的弱直积分解
Weak Direct Product Decompositions of Lattices Generated Finite-Wisely by co-Primes
  
DOI:10.3770/j.issn:1000-341X.2000.02.027
中文关键词:  并素元有限生成格  弱直积分解  完全Heyting代数  Boole代数.
英文关键词:lattice generated finite-wisely by co-primes  weak direct product decomposition  complete Heyting algebra  Boolean algebra.
基金项目:
作者单位
金晨辉 郑州电子技术学院 
摘要点击次数: 2005
全文下载次数: 1407
中文摘要:
      本文建立了并素元有限生成格的弱直积分解,并给出一个解决并素元生成的完全Heyting代数的直积分解问题的新方法;作为弱直积分解的应用,证明了并素元有限生成的完全Heyting代数必然同构于有限个既约的完全Heyting代数的直积,证明了并素元有限生成格是Boole代数的充要条件是它同构于某有限集的幂集格.
英文摘要:
      In this paper, we establish the weak direct product decompositions of lattices generated finite-wisely by co-primes, and solve the problem of direct product decompositions of complete Heyting algebras generated by co-primes in a new way. As applications, we prove that complete Heyting algebras generated finite-wisely by co-primes are isomorphic to the direct product of finite many irreducible complete Heyting algebras, and prove that a lattice generated finite-wisely by co-primes is a Boolean algebra if and only if it's isomorphic to the power set lattice of a finite set.
查看全文  查看/发表评论  下载PDF阅读器