المثاليات والمقاسات الإبتدائية المعرفة على الحلقات غير الإبدالية

Abstract

The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this article we generalize these concepts and introduce the concepts of primary ideals and primary modules over noncommutative rings. Also we give equivalent definitions of primary ideals over noncommutative rings. Finally, we study some properties of primary submodules over noncommutative rings. Key Words: Primary ideals over noncommutative rings, radical annihilator of an R-module, prime modules over noncommutative rings, primary modules over noncommutative rings, primary submodules over noncommutative rings.