IJPAM: Volume 31, No. 3 (2006)


Guoyin Zhang
Department of Basic Courses
Jinling Institute of Technology
314 Baixia Road, Nanjing, 210001, P.R. CHINA
e-mail: gyzhang@jit.edu.cn

Abstract.Let $R$ be any ring with identity. A right $R$-module $M$ is called a top module if $\Spec_{r}(M)$ is a space with Zariski topology. In this paper it will be showed that a right semi-simple module $M$ over a right quasi-duo ring $R$ is top if and only if it is distributive. If $R$ is a right quasi-duo, right perfect ring and $M$ is a right top $R$-module, then it is cyclic. In addition, several known results on the multiplication modules are extended to top modules.

Received: June 29, 2006

AMS Subject Classification: 16S02, 16D11, 54A03

Key Words and Phrases: top module, prime submodule, Zariski topology, uniserial module

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 3