On congruences of weak lattices

详细信息    查看全文

• 作者：Ivan Chajda ; Helmut Länger
• 关键词：Weak lattice ; Congruence ; Majority term
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：20
• 期：12
• 页码：4767-4771
• 全文大小：404 KB
• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479
• 卷排序：20

文摘

We characterize when an equivalence relation on the base set of a weak lattice \(\mathbf{L}=(L,\sqcup ,\sqcap )\) becomes a congruence on \(\mathbf{L}\) provided it has convex classes. We show that an equivalence relation on L is a congruence on \(\mathbf{L}\) if it satisfies the substitution property for comparable elements. Conditions under which congruence classes are convex are studied. If one fundamental operation of \(\mathbf{L}\) is commutative then \(\mathbf{L}\) is congruence distributive and all congruences of \(\mathbf{L}\) have convex classes.