Normal Subloops in the Integral Loop Ring of an RA Loop
Canadian mathematical bulletin, Tome 44 (2001) no. 1, pp. 27-35

Voir la notice de l'article provenant de la source Cambridge University Press

We show that an $\text{RA}$ loop has a torsion-free normal complement in the loop of normalized units of its integral loop ring. We also investigate whether an $\text{RA}$ loop can be normal in its unit loop. Over fields, this can never happen.
DOI : 10.4153/CMB-2001-005-7
Mots-clés : 20N05, 17D05, 16S34, 16U60
Goodaire, Edgar G.; Milies, César Polcino. Normal Subloops in the Integral Loop Ring of an RA Loop. Canadian mathematical bulletin, Tome 44 (2001) no. 1, pp. 27-35. doi: 10.4153/CMB-2001-005-7
@article{10_4153_CMB_2001_005_7,
     author = {Goodaire, Edgar G. and Milies, C\'esar Polcino},
     title = {Normal {Subloops} in the {Integral} {Loop} {Ring} of an {RA} {Loop}},
     journal = {Canadian mathematical bulletin},
     pages = {27--35},
     year = {2001},
     volume = {44},
     number = {1},
     doi = {10.4153/CMB-2001-005-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-005-7/}
}
TY  - JOUR
AU  - Goodaire, Edgar G.
AU  - Milies, César Polcino
TI  - Normal Subloops in the Integral Loop Ring of an RA Loop
JO  - Canadian mathematical bulletin
PY  - 2001
SP  - 27
EP  - 35
VL  - 44
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-005-7/
DO  - 10.4153/CMB-2001-005-7
ID  - 10_4153_CMB_2001_005_7
ER  - 
%0 Journal Article
%A Goodaire, Edgar G.
%A Milies, César Polcino
%T Normal Subloops in the Integral Loop Ring of an RA Loop
%J Canadian mathematical bulletin
%D 2001
%P 27-35
%V 44
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-005-7/
%R 10.4153/CMB-2001-005-7
%F 10_4153_CMB_2001_005_7

[CG86] [CG86] Chein, Orin and Goodaire, Edgar G., Loops whose loop rings are alternative. Comm. Algebra (2) 14 (1986), 293–310. Google Scholar

[dBJ97] [dBJ97] de Barros, Luiz G. X. and Juriaans, Stanley O., Units in alternative integral loop rings. Resultate Math. 31 (1997), 266–281. Google Scholar

[GJM96] [GJM96] Goodaire, E. G., Jespers, E., and Milies, C. Polcino, Alternative loop rings, North-Holland Math. Studies 184, Elsevier, Amsterdam, 1996. Google Scholar

[GM89] [GM89] Goodaire, Edgar G. and Milies, César Polcino, Torsion units in alternative loop rings. Proc. Amer.Math. Soc. 107 (1989), 7–15. Google Scholar

[GM95] [GM95] Goodaire, Edgar G. and Milies, César Polcino, On the loop of units of an alternative loop ring. Nova J. AlgebraGeom. (3) 3 (1995), 199–208. Google Scholar

[GM96a] [GM96a] Goodaire, Edgar G. and Milies, César Polcino, Finite conjugacy in alternative loop algebras. Comm. Algebra (3) 24 (1996), 881–889. Google Scholar

[GM96b] [GM96b] Goodaire, Edgar G. and Milies, César Polcino, Finite subloops of units in an alternative loop ring. Proc. Amer.Math. Soc. (4) 124 (1996), 995–1002. Google Scholar

[Goo95] [Goo95] Goodaire, Edgar G., The radical of a modular alternative loop algebra. Proc. Amer. Math. Soc. (11) 123 (1995), 3289–3299. Google Scholar

[GP86] [GP86] Goodaire, Edgar G. and Parmenter, M. M., Units in alternative loop rings. Israel J. Math. (2) 53 (1986), 209–216. Google Scholar

[GP87] [GP87] Goodaire, Edgar G. and Parmenter, M. M., Semi-simplicity of alternative loop rings, Acta Math. Hungar. (3–4) 50 (1987), 241–247. Google Scholar

[Hig40] [Hig40] Graham Higman, The units of group rings. Proc. LondonMath. Soc. (2) 46 (1940), 231–248. Google Scholar

[JL93] [JL93] Eric Jespers and Guilherme Leal, A characterization of the unit loop of the integral loop ring Z[M16 (Q, 2)]. J. Algebra (1) 155 (1993), 95–109. Google Scholar

[MZ] [MZ] Milies, C. Polcino and Zatelli, Albertina, Nilpotent elements and ideals in alternative loop rings. East West J. Math., to appear. Google Scholar

[Pai56] [Pai56] Paige, Lowell J., A class of simple Moufang loops. Proc. Amer. Math. Soc. 7 (1956), 471–482. Google Scholar

[RS83] [RS83] Roggenkamp, K. W. and Scott, L. L., Units in metabelian group rings: non-splitting examples for normalized units. J. Pure Appl. Algebra 27 (1983), 299–314. Google Scholar

[Seh78] [Seh78] Sehgal, S. K., Topics in group rings, Marcel Dekker, New York, 1978. Google Scholar

[Whi68] [Whi68] Whitcomb, A., The group ring problem, Ph.D. thesis, Chicago, 1968. Google Scholar

[ZSSS82] [ZSSS82] Zhevlakov, K. A., Slin’ko, A. M., Shestakov, I. P., and Shirshov, A. I., Rings that are nearly associative. Academic Press, New York, 1982, translated by Harry F. Smith. Google Scholar

Cité par Sources :