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

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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.

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Last modified: January 27, 2000