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BG/BF1/B/BM-algebras are congruence permutable

Andrzej Walendziak

We show that every pair of congruences on a BG-algebra (also on a BF1/B/BM-algebra) permutes. This result implies that if A is a BG/BF1/B/BM-algebra, then the lattice of all congruences on A is modular. Moreover, it is proved that BF-algebras and BCK-algebras (BCI/BCH/BH-algebras, too) are not congruence permutable, in general.