| Title:
|
Moufang loops arising from Zorn vector matrix algebras (English) |
| Author:
|
Wells, Andrew |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
371-388 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In ``A class of simple Moufang loops'', Proc. Amer. Math. Soc. {\bf 7} (1956), 471--482, Paige used the vector matrix construction over fields to produce simple Moufang loops. The purpose of this paper is to generalize the construction to the class of commutative rings, and examine the Moufang loops arising in this fashion. Specific attention is paid to the construction over the ring of integers modulo four. (English) |
| Keyword:
|
Zorn vector matrix |
| Keyword:
|
Moufang loop |
| Keyword:
|
Paige loop |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20068 |
| idMR:
|
MR2682488 |
| . |
| Date available:
|
2014-07-30T05:58:09Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140113 |
| . |
| Reference:
|
[1] Bruck R.H., Kleinfeld E.: The structure of alternative division rings.Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 88–90; MR0041834 (13,8c). Zbl 0044.02205, MR 0041834, 10.1073/pnas.37.2.88 |
| Reference:
|
[2] Chein O.: Moufang loops of small order. I.Trans. Amer. Math. Soc. 188 (1974), 31–51; MR0330336 (48 \#8673). Zbl 0286.20088, MR 0330336 |
| Reference:
|
[3] Liebeck M.W.: The classification of finite simple Moufang loops.Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 1, 33–47; MR886433 (88g:20146). Zbl 0622.20061, MR 0886433, 10.1017/S0305004100067025 |
| Reference:
|
[4] Merlini Giuliani M.L., Polcino Milies C.: The smallest simple Moufang loop.J. Algebra 320 (2008), no. 3, 961–979; MR2427625 (2009e:20145). Zbl 1157.20041, MR 2427625, 10.1016/j.jalgebra.2007.03.049 |
| Reference:
|
[5] Moufang R.: Zur Struktur von Alternativkörpern.Math. Ann. 110 (1935), no. 1, 416–430; MR1512948. Zbl 0010.00403, MR 1512948, 10.1007/BF01448037 |
| Reference:
|
[6] Paige L.J.: A class of simple Moufang loops.Proc. Amer. Math. Soc. 7 (1956), 471–482; MR0079596 (18,110f). Zbl 0070.25302, MR 0079596, 10.1090/S0002-9939-1956-0079596-1 |
| Reference:
|
[7] Vojtěchovský P.: Investigation of subalgebra lattices by means of Hasse constants.Algebra Universalis 50 (2003), no. 1, 7–26; MR2026823 (2004j:20128). MR 2026823, 10.1007/s00012-003-1804-6 |
| . |
