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 |
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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. |
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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. |
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