Stone Duality for Skew Boolean Algebras with Intersections

Details Stone Duality for Skew Boolean Algebras with Intersections Stone Duality for Skew Boolean Algebras with Intersections

2011-06-02

arxiv.org/abs/1106.0425v1

Mathematics

Rings and Algebras

Scientific paper

We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean algebras with intersections is dual to the category of surjective etale maps between Boolean spaces. We then extend the duality to skew Boolean algebras with intersections, and consider several variations in which the morphisms are restricted. Finally, we use the duality to construct a right-handed skew Boolean algebra without a lattice section.

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