FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 4, PAGES 1229-1237
A. M. Tchernev
Abstract
View as HTML
View as gif image
View as LaTeX source
In this paper author investigates the properties
of PI-rings having faithful module with
Krull dimension relative to a noetherian torsion theory.
The main results of this paper:
Let $R$ be an associative PI-ring
with identity, M be a left faithful $R$ -module,
$\tau$ --- noetherian torsion theory.
Let $\tau M = 0$ and module $M$ have $\tau$ -Krull dimension.
If $N$ is a nil ideal then there exists a natural $n$
such that ${N}^{n}M = 0$ .
Let $R$ be an associative PI-ring with identity,
$M$ be a left faithful $R$ -module,
$\tau$ --- noetherian torsion theory.
Let module $M$ have $\tau$ -Krull dimension.
If $R$ is $\tau$ -torsionfree as left $R$ -module,
module $M$ and prime radical of $R$ are finitely generated,
then $R$ has left $\tau$ -Krull dimension and
left $\tau$ -Krull dimension of $R$ is equal to
left $\tau$ -Krull dimension of module $M$ .
All articles are published in Russian.
Main page | Contents of the journal | News | Search |
Location: http://mech.math.msu.su/~fpm/eng/97/974/97420t.htm
Last modified: January 27, 2000