Graded weakly prime ideals of non-commutative rings

Abstract

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several properties are given, and several examples to support given propositions are constructed. We initiate the study of graded weakly total prime ideals and investigate graded rings for which every proper graded ideal is graded weakly total prime.

Keywords:

• Graded prime ideals
• graded total prime ideals
• graded weakly prime ideals
• graded weakly total prime ideals

2020 Mathematics Subject Classification:

• 16W50
• 13A02

Acknowledgements

The authors gratefully thank the referees for the constructive comments, corrections and suggestions which definitely help to improve the readability and quality of the article.

Additional information

Funding

This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program.