Scalar extensions for algebraic structures of Lukasiewicz logic

Abstract

In this paper we study the tensor product for MV-algebras, the algebraic structures of Łukasiewicz $\infty$-valued logic. Our main results are: the proof that the tensor product is preserved by the categorical equivalence between the MV-algebras and abelian lattice-order groups with strong unit and the proof of the scalar extension property for semisimple MV-algebras. We explore consequences of this results for various classes of MV-algebras and lattice-ordered groups enriched with a product operation.

References in corpus (1)

• Towards understanding the Pierce-Birkhoff conjecture via MV-algebras

Cited by in corpus (2)

• Notes on divisible MV-algebras
• Notes on MV-modules over integral domains