Bogdana Oliynyk: Locally Standard Measure Algebras

Bogdana Oliynyk (Silesian University of Technology): Locally Standard Measure Algebras

We study the classification of countable locally standard Boolean measure algebras. In particular, we provide a parametrization of such algebras: in the unital case by a single Steinitz number, and in the non-unital case by a pair consisting of a Steinitz number and a real parameter greater than or equal to 1.We also show that any unital countable locally standard Boolean measure algebra can be realized as the Boolean algebra of idempotents of a Cartan subalgebra of a locally matrix algebra. The talk is based on joint work with Oksana Bezushchak.