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Keywords:
closure ring; commuting idempotents; central idempotents; Baer ring
closure ring; commuting idempotents; central idempotents; Baer ring
Summary:
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.
References:
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[4] Picavet G.: Ultrafiltres sur un espace spectral-anneaux de Baer-anneaux à spectre minimal compact. Math. Scand. 46 (1980), 23-25. MR 0585229 | Zbl 0491.13003
[5] Rasiowa H.: An Algebraic Approach to Non-Classical Logics. North-Holland, 1974. MR 0446968 | Zbl 0299.02069
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