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 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 …

Full article: The ϕ-Krull dimension of some commutative extensions Skip to Main Content
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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 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 …

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

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

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 …

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 …

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 …