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.
@article{119098, author = {Barry J. Gardner and Tim Stokes}, title = {Closure rings}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {40}, year = {1999}, pages = {413-427}, zbl = {1014.16019}, mrnumber = {1732493}, language = {en}, url = {http://dml.mathdoc.fr/item/119098} }
Gardner, Barry J.; Stokes, Tim. Closure rings. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 413-427. http://gdmltest.u-ga.fr/item/119098/
Linear Algebra and Projective Geometry, Academic Press, New York, 1952. | MR 0052795 | Zbl 0049.38103
Rings of Operators, W.A. Benjamin Inc., New York and Amsterdam, 1968. | MR 0244778 | Zbl 0174.18503
Algebra of topology, Ann. Math. 45 (1944), 141-191. (1944) | MR 0009842 | Zbl 0060.06206
Ultrafiltres sur un espace spectral-anneaux de Baer-anneaux à spectre minimal compact, Math. Scand. 46 (1980), 23-25. (1980) | MR 0585229 | Zbl 0491.13003
An Algebraic Approach to Non-Classical Logics, North-Holland, 1974. | MR 0446968 | Zbl 0299.02069