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ON CHAINS OF CLASSICAL PRIME SUBMODULES AND DIMENSION THEORY OF
MODULES† Communicated by Siamak Yassemi 1. Introduction The cl Page 1 Bulletin of the …

This memoir is devoted to the study of Krull dimensions of modules over (not necessarily
commutative) rings with identity. Although not all modules have a Krull dimension …

DUAL RELATIVE KRULL DIMENSION OF MODULES OVER COMMUTATIVE RINGS and The
concept of Krull dimension k(E) of an arbitrary poset (E Page 1 DUAL RELATIVE KRULL …

A krull-like dimension for noncommutative rings Page 1 A KRULL-LIKE DIMENSION FOR
NONCOMMUTATIVE RINGS BY JONATHAN S. GOLAN ABSTRACT Let R be an associative …

In this article, we introduce and study a generalization of the classical Krull dimension for a
module MR. This is defined to be the length of the longest strong chain of prime submodules …

The notion of Krull dimension of a ring (commutative with identity) is of great importance in
the field of commutative algebra. In particular, the study of dimension behavior in ring …

Let R be a commutative ring with identity. We show that the Krull dimension of the power
series ring R [X] can be uncountably infinite, ie, there exists an uncountably infinite chain of …

THE KRULL-GABRIEL DIMENSION OF AN ALGEBRA - OPEN PROBLEMS AND
CONJECTURES Page 1 Trends in Mathematics, © 2000 Birkhiiuser Verlag Basel/Switzerland …

In this article, we introduce and study the concepts of non-small Krull dimension and non-
small Noetherian dimension of an R-module M, where R is an arbitrary associative ring …