Abstract
LetG be a group andA aG-graded ring. A (graded) idealI ofA is (graded) essential ifI⊃J≠0 wheneverJ is a nonzero (graded) ideal ofA. In this paper we study the relationship between graded essential ideals ofA, essential ideals of the identity componentAe and essential ideals of the smash productA#G*. We apply our results to prime essential rings, irredundant subdirect sums and essentially nilpotent rings.
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