A note on congruences of semilattices with sectionally finite height

作者：Maria Font Josep; Moraschini Tommaso

来源：Algebra Universalis, 2014, 72(3): 287-293.

DOI：10.1007/s00012-014-0300-5

• semilattices
• congruences
• sectionally finite height
• rainbows
• clouds
• Leibniz operator
• abstract algebraic logic

We present a bijective correspondence between congruences of semilattices with sectionally finite height (i.e., meet-semilattices whose principal downsets have finite length) and certain special subsets of their universes. We characterize these subsets from a purely order-theoretic point of view and prove that the bijection coincides with the Leibniz operator of abstract algebraic logic.

• 出版日期2014-11