SOME PROPERTIES OF PRIME MODULE AND SEMIPRIME MODULE

• Main Author: Puspitorini, Mega
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/39060
• Institution: Institut Teknologi Bandung

Prime module was introduced by Feller and Swokowski (1965). In 1978, J. Da- uns did a research about generalization of prime module and defined semiprime module as weaker terms of prime module. In other hand, Abu-Saymeh (1995) studied characteristic ring of prime (semiprime) module. Furthermore Behbo- odi, Karamzadeh, and Koohy (2003) defined almost prime module, fully prime (semiprime) module, and almost fully prime (semiprime) module. Necessary and sufficient conditions for those type of module was also given. In this thesis, we will discuss the result of Behboodi, et al. (2003) those are necessary and sufficient condition for almost prime module, fully prime (semiprime) module, and almost fully prime (semiprime) module. Then the relation between prime module and semiprime module is studied. At the end, we will prove a new theorem about necessary and sufficient conditions for semiprime module to be a prime module.