JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 1, Pages 47 - 58
(June 2008)
|
|
ON PRIME SUBMODULES
Yi Qiu (P. R. China)
|
Abstract: In this paper, we study the properties of prime submodules of a finite module over a Noetherian local ring. The results of the paper show that the properties of such prime submodules are similar to that of prime ideals. We will prove a prime avoidance theorem for prime submodules under a slight weaker assumption. Moreover, we will give an upper bound for the length of ascending chains of prime submodules of a finite module. |
Keywords and phrases: prime ideal, prime submodule, Noetherian local ring. |
|
Number of Downloads: 442 | Number of Views: 1195 |
|