I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 4, PAGES 1107-1121
On the uniform dimension of skew polynomial rings in many variables
V. A. Mushrub
View as HTML
View as gif image
View as LaTeX source
an associative ring, be
a nonempty set of variables, be a family
of injective ring endomorphisms of and be the Cohn--Jordan
In this paper we prove that the left uniform dimension of
the skew polynomial ring is equal to
the left uniform dimension of , provided that
for all nonzero .
Furthermore, we show that for semiprime rings the equality
does not hold in the general case.
The following problem is still open.
Does hold if
a semiprime ring, is an injective ring
endomorphism of and ?
All articles are
published in Russian.
Last modified: April 17, 2002