Rings Graded By a Generalized Group

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. Weprove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We...

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Main Authors:	Fatehi Farzad, Molaei Mohammad Reza
Format:	Article
Language:	English
Published:	De Gruyter 2014-01-01
Series:	Topological Algebra and its Applications
Subjects:	completely simple semigroup grading graded ring maximal ideal homogeneous ideal 16w99 13a99
Online Access:	https://doi.org/10.2478/taa-2014-0005

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spelling	doaj-45ad4d50bc934203bf81b57a90eb623f2021-10-02T19:17:47ZengDe GruyterTopological Algebra and its Applications2299-32312014-01-012110.2478/taa-2014-0005taa-2014-0005Rings Graded By a Generalized GroupFatehi Farzad0Molaei Mohammad Reza1Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, IranDepartment of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, IranThe 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..https://doi.org/10.2478/taa-2014-0005completely simple semigroup grading graded ring maximal ideal homogeneous ideal16w9913a99
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fatehi Farzad Molaei Mohammad Reza
spellingShingle	Fatehi Farzad Molaei Mohammad Reza Rings Graded By a Generalized Group Topological Algebra and its Applications completely simple semigroup grading graded ring maximal ideal homogeneous ideal 16w99 13a99
author_facet	Fatehi Farzad Molaei Mohammad Reza
author_sort	Fatehi Farzad
title	Rings Graded By a Generalized Group
title_short	Rings Graded By a Generalized Group
title_full	Rings Graded By a Generalized Group
title_fullStr	Rings Graded By a Generalized Group
title_full_unstemmed	Rings Graded By a Generalized Group
title_sort	rings graded by a generalized group
publisher	De Gruyter
series	Topological Algebra and its Applications
issn	2299-3231
publishDate	2014-01-01
description	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. 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..
topic	completely simple semigroup grading graded ring maximal ideal homogeneous ideal 16w99 13a99
url	https://doi.org/10.2478/taa-2014-0005
work_keys_str_mv	AT fatehifarzad ringsgradedbyageneralizedgroup AT molaeimohammadreza ringsgradedbyageneralizedgroup
_version_	1716847347139346432

Rings Graded By a Generalized Group

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