دراسة الـPI – حلقات في التدريج وفق نصف زمرة

Abstract

In this research, we have studied the relationship between graded ring by semigroup and it is grading components and that is when the graded ring is PI-Ring or the components are PI-Rings.  Where in this study we have graded the rings by special types of semigroups such as left regular band and completely regular semigroup. We have also studied some properties of nil-clean graded rings and their relationship to PI-Rings.