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Lie rings; commutative associative rings
Let $K$ be an associative and commutative ring with $1$, $k$ a subring of $K$ such that $1\in k$, $n\geq 2$ an integer. The paper describes subrings of the general linear Lie ring $gl_{n} ( K )$ that contain the Lie ring of all traceless matrices over $k$.
[1] Bashkirov E.L.: Matrix Lie rings that contain a one-dimensional Lie algebra of semi-simple matrices. J. Prime Res. Math. 3 (2007), 111–119. MR 2397770
[2] Bashkirov E.L.: Matrix Lie rings that contain an abelian subring. J. Prime Res. Math. 4 (2008), 113–117. MR 2490007
[3] Wang D.Y.: Extensions of Lie algebras according to the extension of fields. J. Math. Res. Exposition 25 (2005), no. 3, 543–547. MR 2163737
[4] Zhao Y.X., Wang D.Y., Wang Ch.H.: Intermediate Lie algebras between the symplectic algebras and the general linear Lie algebras over commutative rings. J. Math. (Wuhan) 29 (2009), no. 3, 247-252. MR 2541763
[5] Vavilov N.A.: Intermediate subgroups in Chevalley groups. Groups of Lie Type and Their Geometries (Como 1993), London Math. Soc. Lecture Note Ser., 207, Cambridge Univ. Press, Cambridge, 1995, pp. 233–280. MR 1320525
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