The 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. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..
@article{bwmeta1.element.doi-10_2478_taa-2014-0005,
author = {Farzad Fatehi and Mohammad Reza Molaei},
title = {Rings Graded By a Generalized Group},
journal = {Topological Algebra and its Applications},
volume = {2},
year = {2014},
zbl = {1306.16043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2014-0005}
}
Farzad Fatehi; Mohammad Reza Molaei. Rings Graded By a Generalized Group. Topological Algebra and its Applications, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2014-0005/
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