Abstract:We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central idempotents.
Keywords: closure ring, commuting idempotents, central idempotents, Baer ring
AMS Subject Classification: 16W99