Closure rings

Barry J. Gardner; Tim Stokes

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 413-427
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Gardner, Barry J., and Stokes, Tim. "Closure rings." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 413-427. <http://eudml.org/doc/248422>.

@article{Gardner1999,
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.},
author = {Gardner, Barry J., Stokes, Tim},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {closure ring; commuting idempotents; central idempotents; Baer ring; closure rings; commuting idempotents; central idempotents; Baer rings; normal filters; closed ideals; closure operations},
language = {eng},
number = {3},
pages = {413-427},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Closure rings},
url = {http://eudml.org/doc/248422},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Gardner, Barry J.
AU - Stokes, Tim
TI - Closure rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 413
EP - 427
AB - 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.
LA - eng
KW - closure ring; commuting idempotents; central idempotents; Baer ring; closure rings; commuting idempotents; central idempotents; Baer rings; normal filters; closed ideals; closure operations
UR - http://eudml.org/doc/248422
ER -

References

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  1. Baer R., Linear Algebra and Projective Geometry, Academic Press, New York, 1952. Zbl0049.38103MR0052795
  2. Kaplansky I., Rings of Operators, W.A. Benjamin Inc., New York and Amsterdam, 1968. Zbl0174.18503MR0244778
  3. McKinsey J.C.C., Tarski A., Algebra of topology, Ann. Math. 45 (1944), 141-191. (1944) Zbl0060.06206MR0009842
  4. Picavet G., Ultrafiltres sur un espace spectral-anneaux de Baer-anneaux à spectre minimal compact, Math. Scand. 46 (1980), 23-25. (1980) Zbl0491.13003MR0585229
  5. Rasiowa H., An Algebraic Approach to Non-Classical Logics, North-Holland, 1974. Zbl0299.02069MR0446968

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