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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.8298
- arXiv:
- arXiv:1410.8298
- Bibcode:
- 2014arXiv1410.8298L
- Keywords:
-
- Mathematics - Logic
- E-Print:
- Journal of Pure and Applied Algebra, 220 (2016) 1538-1553