1122-06-205
Vincenzo Marra* ([email protected]), Dipartimento di Matematica F. Enriques,
Università degli Studi di Milano, via Cesare Saldini 50, 20133 Milan, Italy. Separability for
lattice-ordered Abelian groups and MV-algebras: a characterisation theorem.
This is joint work with Matias Menni (CONICET, Argentina). The classical notion of separable algebra has been
abstracted to any category satisfying certain assumptions. See A. Carboni and G. Janelidze, J. Pure and Applied
Algebra, 110(1996) no. 3, 219–240. This leads to a notion of separable lattice-ordered Abelian group with a strong unit,
or equivalently, separable MV-algebra. Theorem: An MV-algebra is separable if, and only if, it is (isomorphic to) a finite
product of subalgebra of [0, 1] ∩ Q, the MV-algebra of rational numbers. The proof of this purely algebraic result is
substantial; I will sketch it in the available time. Motivation: The result provides foundations for the current programme
of extending the algebraic geometry of Baker-Beynon duality from coefficients in Z (lattice-groups, or MV-algebras) to
coefficients in an arbitrary ordered subring of the reals, i.e. in a simple extension of Z. The largest possible such extension,
the reals, corresponds to vector lattices. The result presented here identifies simple separable extensions of Z amongst all
extensions as precisely the rational ones. (Received August 14, 2016)
1
