The Tensor PMV-algebra of an MV-algebra

Abstract

The classical construction of tensor algebra is done in the context of MV-algebras. We construct the tensor PMV-algebra of an MV-algebra, which yields an adjunction between the category of MV-algebras and the category of PMV-algebras. In particular, for any MV-algebra A, the tensor PMV-algebra of A is the free PMV-algebra over A.