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Title: Closure rings (English)
Author: Gardner, B. J.
Author: Stokes, Tim
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 40
Issue: 3
Year: 1999
Pages: 413-427
Category: math
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. (English)
Keyword: closure ring
Keyword: commuting idempotents
Keyword: central idempotents
Keyword: Baer ring
MSC: 03G05
MSC: 06A15
MSC: 06E20
MSC: 16N20
MSC: 16W99
idZBL: Zbl 1014.16019
idMR: MR1732493
Date available: 2009-01-08T18:53:39Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Baer R.: Linear Algebra and Projective Geometry.Academic Press, New York, 1952. Zbl 0049.38103, MR 0052795
Reference: [2] Kaplansky I.: Rings of Operators.W.A. Benjamin Inc., New York and Amsterdam, 1968. Zbl 0174.18503, MR 0244778
Reference: [3] McKinsey J.C.C., Tarski A.: Algebra of topology.Ann. Math. 45 (1944), 141-191. Zbl 0060.06206, MR 0009842
Reference: [4] Picavet G.: Ultrafiltres sur un espace spectral-anneaux de Baer-anneaux à spectre minimal compact.Math. Scand. 46 (1980), 23-25. Zbl 0491.13003, MR 0585229
Reference: [5] Rasiowa H.: An Algebraic Approach to Non-Classical Logics.North-Holland, 1974. Zbl 0299.02069, MR 0446968


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