On the relationship between AP, RS and CEP

Kearnes, Keith A.

doi:10.1090/S0002-9939-1989-0952317-5

On the relationship between AP, RS and CEP
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Proc. Amer. Math. Soc. 105 (1989), 827-839 Request permission

Abstract:

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.

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