On Rings Whose Principal Ideals are Generalized Pure Ideals

Abstract

This paper , introduces the notion of a right PIGP-ring (a ring in which every principal ideal of R is a GP-ideal ) with some of their basic properties ; we also give necessary and sufficient conditions for PIGP-rings to be a division ring and a regular ring .

Keywords

• generalized pure ideal
• principal ideal
• divisor rings
• regular rings