College of Science, Shiraz University, Shiraz 71454, Iran. Page 1 Honam Mathematical J. 21(1999),
No. 1, pp. 1-12 ON PRIME SUBMODULES A. AZIZI AND H. SHARIF Dept. of Mathematics …

In order to compute the Krull dimension of a module it is useful to have a comparison
between the Krull dimensions of the module and its submodules. One of the basic results in …

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

In this paper, we study the dimension of a module over a commutative ring, which is defined
to be the length of a longest chain of prime submodules. This notion is analogous to the …

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 …

We introduce and study the concept of small Krull dimension of a module which is Krull-like
dimension extension of the concept of DCC on small submodules. Using this concept we …

In this paper, all rings are commutative with identity and all modules are unitary. Let R be a
ring and M an R-module. A proper submodule N of M is said to be prime (or P-prime) if rm …

Rings And Modules With Krull Dimension Page 1 Rings And Modules With Krull Dimension by
Alex Woodward A thesis submitted to the Faculty of Information and Mathematical Sciences at …

Recently several studies have been made concerning Z-graded commu tative rings and
their graded modules. For example Iversen [6] has used the theory of graded modules and …

The formula dim (A+ B)= dim (A)+ dim (B)-dim (A∩ B) works when 'dim'stands for the
dimension of subspaces A, B of any vector space. In general, however, it does no longer …