On the minimal extension of the sequence $ \langle 0,1,1,7 \rangle $

Abstract.

This note shows that the p _n -sequence \( \langle 0,1,1,7 \rangle \) has the minimal extension property in the class of algebras with a nonassociative binary operation. This generalizes the result of J. Galuszka and gives a partial solution of problem 18 raised by G. Grätzer and A. Kisielewicz of whether \( \langle 0,1,1,7 \rangle \) has the minimal extension property. This result reduces the problem to the class of algebras with a semilattice operation.