IJPAM: Volume 26, No. 4 (2006)

A NOTE ON APN-RINGS

N. Amiri$^1$, H. Jafarpour$^2$
$^{1,2}$Department of Mathematics
Azad University of Firoozabad
Firoozabad, IRAN
$^1$e-mail: amiri@susc.ac.ir
$^2$e-mail: Hydeh.Jafarpour@gmail.com


Abstract.Throughout this paper $R$ is a commutative ring with identity and all modules are unitary. It is well known that an Artinian ring with identity is a Noetherian. But an Artinian module is not Noetherian and a Noetherian module is not Artinian in general. In this paper we have some results for rings whose Artinian modules are Noeteherian modules and Noetherian Modules are Aritinan. Such a rings is called APN-ring.

Received: November 17, 2005

AMS Subject Classification: 13C13, 13C05

Key Words and Phrases: Artinian ring, Noetherian module, APN-ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4