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arXiv · 2307.03978

Separable MV-algebras and lattice-groups

Vincenzo Marra·Matías Menni
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Abstract

General theory determines the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers, i.e., of subalgebras of the MV-algebra $[0,1]\cap\mathbb{Q}$. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the categroy of MV-algebras, in analogy with the classical case of commutative $K$-algebras over a field $K$.

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Vincenzo Marra, Matías Menni. 2023-07-08. Separable MV-algebras and lattice-groups. https://arxiv.org/abs/2307.03978

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