关于蕴含格的一些注记

Notes on the Implicative Lattices

本文证明了当蕴含格作为L-代数时,其L-理想格和L-同余格是同构的以及L-同余格与它作为蕴含格的同余格也是同构的。进一步给出了Heyting代数中同余关系更一般的简化。

In this paper, we prove that L-ideals lattice and L-congruences lattice are isomorphic when the implicative lattice is an L-algebra, and L-congruences lattice is isomorphic to its congruences lattice when L is an implicative lattice. Furthermore, a more general simplification of congruence relations in Heyting algebras is given.