FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1995, VOLUME 1, NUMBER 3, PAGES 661-668
On the general linear group over weak Noetherian associative algebras
I.Z.Golubchik
Let R be a
weak Noetherian algebra with unity element over an infinite field,
I
an ideal in R,
$n \geq 3$,
En(R)
the elementary subgroup in the general linear
group GLn(R),
En(R,I)
the normal subgroup
in En(R)
generated by the elementary matrices
$1 + \lambda e_{ij}$,
$\lambda \in I$,
$1 \leq i \neq j \leq n$,
GLn(R,I)
the kernel and Cn(R,I)
the preimage of the center of the homomorphism
$GL_n(R) \to GL_n(R/I)$
respectively. It is proved that if G is
a subgroup
of GLn(R),
then it is normalized
by En(R) if
and only if
$E_n(R,F) \subseteq G \subseteq C_n(R,F)$
for some ideal F
of R;
[Cn(R,F),En(R)]
= En(R,F)
and in particular
the groups En(R)
and En(R,F)
are
normal in GLn(R)
for all ideals F
of R.
All articles are
published in Russian.
Location: http://mech.math.msu.su/~fpm/eng/95/953/95307.htm
Last modified: October 10, 1997.