| 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:
|
http://hdl.handle.net/10338.dmlcz/119098 |
| . |
| 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 |
| . |
