Moufang loops arising from Zorn vector matrix algebras
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 2, page 371-388
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topWells, Andrew. "Moufang loops arising from Zorn vector matrix algebras." Commentationes Mathematicae Universitatis Carolinae 51.2 (2010): 371-388. <http://eudml.org/doc/37767>.
@article{Wells2010,
abstract = {In “A class of simple Moufang loops”, Proc. Amer. Math. Soc. 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.},
author = {Wells, Andrew},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Zorn vector matrix; Moufang loop; Paige loop; Zorn vector matrix algebras; Moufang loops; Paige loops},
language = {eng},
number = {2},
pages = {371-388},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Moufang loops arising from Zorn vector matrix algebras},
url = {http://eudml.org/doc/37767},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Wells, Andrew
TI - Moufang loops arising from Zorn vector matrix algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 2
SP - 371
EP - 388
AB - In “A class of simple Moufang loops”, Proc. Amer. Math. Soc. 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.
LA - eng
KW - Zorn vector matrix; Moufang loop; Paige loop; Zorn vector matrix algebras; Moufang loops; Paige loops
UR - http://eudml.org/doc/37767
ER -
References
top- Bruck R.H., Kleinfeld E., 10.1073/pnas.37.2.88, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 88–90; MR0041834 (13,8c). Zbl0044.02205MR0041834DOI10.1073/pnas.37.2.88
- Chein O., Moufang loops of small order. I, Trans. Amer. Math. Soc. 188 (1974), 31–51; MR0330336 (48 #8673). Zbl0286.20088MR0330336
- Liebeck M.W., 10.1017/S0305004100067025, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 1, 33–47; MR886433 (88g:20146). Zbl0622.20061MR0886433DOI10.1017/S0305004100067025
- Merlini Giuliani M.L., Polcino Milies C., 10.1016/j.jalgebra.2007.03.049, J. Algebra 320 (2008), no. 3, 961–979; MR2427625 (2009e:20145). Zbl1157.20041MR2427625DOI10.1016/j.jalgebra.2007.03.049
- Moufang R., 10.1007/BF01448037, Math. Ann. 110 (1935), no. 1, 416–430; MR1512948. Zbl0010.00403MR1512948DOI10.1007/BF01448037
- Paige L.J., 10.1090/S0002-9939-1956-0079596-1, Proc. Amer. Math. Soc. 7 (1956), 471–482; MR0079596 (18,110f). Zbl0070.25302MR0079596DOI10.1090/S0002-9939-1956-0079596-1
- Vojtěchovský P., 10.1007/s00012-003-1804-6, Algebra Universalis 50 (2003), no. 1, 7–26; MR2026823 (2004j:20128). MR2026823DOI10.1007/s00012-003-1804-6
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.