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arXiv · 1410.8298

Scalar extensions for algebraic structures of Lukasiewicz logic

Serafina Lapenta·Ioana Leustean
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Abstract

In this paper we study the tensor product for MV-algebras, the algebraic structures of \L ukasiewicz $\infty$-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.

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Serafina Lapenta, Ioana Leustean. 2014-10-30. Scalar extensions for algebraic structures of Lukasiewicz logic. https://doi.org/10.1016/j.jpaa.2015.09.017

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