| Title:
|
Bol loops with a large left nucleus (English) |
| Author:
|
Chein, Orin |
| Author:
|
Goodaire, Edgar G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
171-196 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Possession of a unique nonidentity commutator/associator is a property which dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an ``interesting'' identity. Indeed, until now, with the exception of some ad hoc examples, the only known class of Bol loops whose loop rings satisfy the right Bol identity have this property. In this paper, we identify another class of loops whose loop rings are ``strongly right alternative'' and present various constructions of these loops. (English) |
| Keyword:
|
Bol loop |
| Keyword:
|
left nucleus |
| Keyword:
|
centre |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1192.20051 |
| idMR:
|
MR2426884 |
| . |
| Date available:
|
2009-05-05T17:07:29Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119714 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[GJM96] Goodaire E.G., Jespers E., Polcino Milies C.: Alternative Loop Rings.North-Holland Math. Studies, vol. 184, Elsevier, Amsterdam, 1996. Zbl 0878.17029, MR 1433590 |
| Reference:
|
[Goo83] Goodaire E.G.: Alternative loop rings.Publ. Math. Debrecen 30 (1983), 31-38. Zbl 0537.17006, MR 0733069 |
| Reference:
|
[GR82] Goodaire E.G., Robinson D.A.: Loops which are cyclic extensions of their nuclei.Compositio Math. 45 (1982), 341-356. Zbl 0488.20057, MR 0656610 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[Moo] Moorhouse G.E.: {{http://everest.uwyo.edu/$^{\sim}$moorhous/pub/bol.html}}.. |
| Reference:
|
[Pai55] Paige L.J.: A theorem on commutative power associative loop algebras.Proc. Amer. Math. Soc. 6 (1955), 279-280. Zbl 0064.02903, MR 0068529, 10.1090/S0002-9939-1955-0068529-9 |
| Reference:
|
[Pfl90] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Heldermann Verlag, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| Reference:
|
[Voj04] Vojtěchovský P.: A class of Bol loops with a subgroup of index two.Comment. Math. Univ. Carolin. 45 (2004), 371-381. Zbl 1101.20048, MR 2075284 |
| . |
