Splittings in Subreducts of Hoops

Abstract

AbstractIn this paper we extend to various classes of subreducts of hoops some results about splitting algebras. In particular we prove that every finite chain in the purely implicational fragment of basic hoops is splitting and that every finite chain in the $$\{\wedge ,\rightarrow \}$$ { ∧ , → } fragment of hoops is splitting. We also produce explicitly the splitting equations in most cases.