Abstract
AbstractThe aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deducea characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if Ris a Noetherian graded ring, then each summand of it is also a Noetherian module..
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