Two remarks on Lie rings of matrices over commutative associative rings
Commentationes Mathematicae Universitatis Carolinae (2020)
- Volume: 61, Issue: 1, page 1-10
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topBashkirov, Evgenii L.. "Two remarks on Lie rings of $2\times 2$ matrices over commutative associative rings." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 1-10. <http://eudml.org/doc/297070>.
@article{Bashkirov2020,
abstract = {Let $C$ be an associative commutative ring with 1. If $a\in C$, then $aC$ denotes the principal ideal generated by $a$. Let $l, m, n$ be nonzero elements of $C$ such that $mn \in lC$. The set of matrices $\left( \{\{\textstyle \begin\{matrix\} a_\{11\} & a_\{12\} a_\{21\} & -a_\{11\} \end\{matrix\}\}\} \right) $, where $a_\{11\}\in lC$, $a_\{12\}\in mC$, $a_\{21\}\in nC$, forms a Lie ring under Lie multiplication and matrix addition. The paper studies properties of these Lie rings.},
author = {Bashkirov, Evgenii L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lie ring; associative commutative ring; matrix},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two remarks on Lie rings of $2\times 2$ matrices over commutative associative rings},
url = {http://eudml.org/doc/297070},
volume = {61},
year = {2020},
}
TY - JOUR
AU - Bashkirov, Evgenii L.
TI - Two remarks on Lie rings of $2\times 2$ matrices over commutative associative rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 1
EP - 10
AB - Let $C$ be an associative commutative ring with 1. If $a\in C$, then $aC$ denotes the principal ideal generated by $a$. Let $l, m, n$ be nonzero elements of $C$ such that $mn \in lC$. The set of matrices $\left( {{\textstyle \begin{matrix} a_{11} & a_{12} a_{21} & -a_{11} \end{matrix}}} \right) $, where $a_{11}\in lC$, $a_{12}\in mC$, $a_{21}\in nC$, forms a Lie ring under Lie multiplication and matrix addition. The paper studies properties of these Lie rings.
LA - eng
KW - Lie ring; associative commutative ring; matrix
UR - http://eudml.org/doc/297070
ER -
References
top- Bashkirov E. L., 10.1080/03081087.2017.1422235, Linear Multilinear Algebra 67 (2019), no. 3, 456–478. MR3909003DOI10.1080/03081087.2017.1422235
- Bashkirov E. L., Pekönür E., On matrix Lie rings over a commutative ring that contain the special linear Lie ring, Comment. Math. Univ. Carolin. 57 (2016), no. 1, 1–6. MR3478334
- Borevich, A. I., Shafarevich I. R., Number Theory, Pure and Applied Mathematics, 20, Academic Press, New York, 1966. MR0195803
- Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Graduate Texts in Mathematics, 84, Springer, New York, 1990. MR1070716
- Koibaev V. A., Nuzhin Ya. N., Subgroups of Chevalley groups and Lie rings of definable by a collection of additive subgroups of the original ring, Fundam. Prikl. Mat. 18 (2013), no. 1, 75–84 (Russian. English, Russian summary); translated in J. Math. Sci. (NY) 201 (2014), no. 4, 458–464. MR3431766
- Nuzhin Ya. N., Lie rings defined by the root system and family of additive subgroups of the initial ring, Proc. Steklov Inst. Math. 283 (2013), suppl. 1, S119–S125. MR3476385
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.