FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 4, PAGES 1229-1237

Nilpotency of prime radical in PI-rings having faithful module with relative Krull dimension

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, t -- noetherian torsion theory. Let t M = 0 and module M have t-Krull dimension. If N is a nil ideal then there exists a natural n such that NnM = 0.

Let R be an associative PI-ring with identity, M be a left faithful R-module, t -- noetherian torsion theory. Let module M have t-Krull dimension. If R is t-torsionfree as left R-module, module M and prime radical of R are finitely generated, then R has left t-Krull dimension and left t-Krull dimension of R is equal to left t-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/97/974/97420h.htm
Last modified: January 27, 2000