IJPAM: Volume 26, No. 4 (2006)
Department of Mathematics
Azad University of Firoozabad
Abstract.Throughout this paper 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