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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2014-01-01
|
| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/taa-2014-0005 |
| Summary: | 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.. |
|---|---|
| ISSN: | 2299-3231 |