  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.
