| Title:
|
Radicals which define factorization systems (English) |
| Author:
|
Gardner, B. J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
601-607 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system. (English) |
| Keyword:
|
radical class |
| Keyword:
|
factorization system |
| MSC:
|
16A21 |
| MSC:
|
16N80 |
| MSC:
|
16S90 |
| MSC:
|
17A65 |
| MSC:
|
18A20 |
| MSC:
|
18E40 |
| idZBL:
|
Zbl 0752.16009 |
| idMR:
|
MR1159806 |
| . |
| Date available:
|
2009-01-08T17:47:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118439 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Fay T.H., Walls G.L.: Categorically compact locally nilpotent groups.Comm. Algebra 18 (1990), 3423-3435. Zbl 0739.20012, MR 1063986 |
| Reference:
|
[5] Gardner B.J.: Some degeneracy and pathology in non-associative radical theory.Annales Univ. Sci. Budapest Sect. Math. 22-23 (1979-80), 65-74. Zbl 0447.17004, MR 0588424 |
| Reference:
|
[6] Gardner B.J.: Radical Theory.Longman, Harlow, 1989. Zbl 1169.16012, MR 1006673 |
| Reference:
|
[7] Herrlich H., Salicrup G., Strecker G.E.: Factorizations, denseness, separation, and relatively compact objects.Topology Appl. 27 (1987), 157-169. Zbl 0629.18003, MR 0911689 |
| Reference:
|
[8] Manes E.G.: Compact Hausdorff objects.General Topology Appl. 4 (1974), 341-360. Zbl 0289.54003, MR 0367901 |
| Reference:
|
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| Reference:
|
[10] Puczylowski E.R.: On unequivocal rings.Acta Math. Acad. Sci Hungar. 36 (1980), 57-62. Zbl 0464.16005, MR 0605170 |
| Reference:
|
[11] Sands A.A.: On ideals in over-rings.Publ. Math. Debrecen 35 (1988), 273-279. Zbl 0688.16035, MR 1005290 |
| Reference:
|
[12] Stewart P.N.: Strict radical classes of associative rings.Proc. Amer. Math. Soc. 39 (1973), 273-278. Zbl 0244.16005, MR 0313296 |
| . |
