On groups of similitudes in associative rings
Commentationes Mathematicae Universitatis Carolinae (2008)
- Volume: 49, Issue: 4, page 525-531
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topBashkirov, Evgenii L.. "On groups of similitudes in associative rings." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 525-531. <http://eudml.org/doc/250452>.
@article{Bashkirov2008,
abstract = {Let $R$ be an associative ring with 1 and $R^\{\times \}$ the multiplicative group of invertible elements of $R$. In the paper, subgroups of $R^\{\times \}$ which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.},
author = {Bashkirov, Evgenii L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {associative rings; unipotent elements; associative rings; unipotent elements; groups of invertible elements; similitudes; isometry groups},
language = {eng},
number = {4},
pages = {525-531},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On groups of similitudes in associative rings},
url = {http://eudml.org/doc/250452},
volume = {49},
year = {2008},
}
TY - JOUR
AU - Bashkirov, Evgenii L.
TI - On groups of similitudes in associative rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 525
EP - 531
AB - Let $R$ be an associative ring with 1 and $R^{\times }$ the multiplicative group of invertible elements of $R$. In the paper, subgroups of $R^{\times }$ which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.
LA - eng
KW - associative rings; unipotent elements; associative rings; unipotent elements; groups of invertible elements; similitudes; isometry groups
UR - http://eudml.org/doc/250452
ER -
References
top- Bashkirov E.L., 10.1007/BF02106733, Siberian Math. J. 37 (1996), 5 754-759. (1996) MR1440380DOI10.1007/BF02106733
- Bashkirov E.L., 10.1016/j.jalgebra.2004.09.006, J. Algebra 287 (2005), 2 319-350. (2005) Zbl1088.20030MR2134148DOI10.1016/j.jalgebra.2004.09.006
- Bashkirov E.L., 10.1080/00927870500454802, Comm. Algebra 34 (2006), 6 1931-1948. (2006) Zbl1110.20038MR2235072DOI10.1080/00927870500454802
- Bashkirov E.L., 10.1080/00927870601074798, Comm. Algebra 35 (2007), 3 1019-1054. (2007) Zbl1118.20049MR2305248DOI10.1080/00927870601074798
- Dieudonné J., La Géométrie des Groups Classiques, Ergebnisser der Mathematik, Springer, Berlin-New York, 1997.
- Dixon J.D., The Structure of Linear Groups, Van Nostrand Reinhold Company, London, 1971. Zbl0232.20079
- Dye R.H., 10.1016/0021-8693(80)90110-6, J. Algebra 66 (1980), 1 1-11. (1980) Zbl0444.20036MR0591244DOI10.1016/0021-8693(80)90110-6
- King O.H., 10.1016/0021-8693(85)90045-6, J. Algebra 96 (1985), 1 178-193. (1985) Zbl0572.20028MR0808847DOI10.1016/0021-8693(85)90045-6
- King O.H., On subgroups of the special linear group containing the special unitary group, Geom. Dedicata 19 (1985), 3 297-310. (1985) Zbl0579.20040MR0815209
- O'Meara O.T., Symplectic Groups, American Mathematical Society, Providence, R.I., 1978. Zbl0383.20001MR0502254
- Zalesskiĭ A.E., Serežkin V.N., Linear groups generated by transvections, Izv. Akad. Nauk SSSR. Ser. Mat. 40 (1976), 1 26-49. (1976) MR0412295
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.