On the relationship between AP, RS and CEP
Keith A. Kearnes · Proceedings of the American Mathematical Society · 1989
We prove that in a residually small congruence modular variety the amalgamation property implies the commutator condition ${\text {R}}$. A consequence of this is that, for all congruence modular varieties, ${\text {AP + RS}}$ implies the CEP. We also show that this implication holds for any variety of semigroups.