A note on intervals of residuated ℓ-groupoids

Dvurečenskij and Hyčko recently proved that every interval of a bounded integral divisible residuated ℓ-monoid can be made into a bounded integral residuated ℓ-monoid. In this note we show that this construction essentially works in the more general setting of integral residuated ℓ-groupoids, and that divisibility is not only sufficient but also necessary.