The extension dimension of group graded rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911270075105280 |
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| author | Luo, Pei Liu, Zhongkui |
| author_facet | Luo, Pei Liu, Zhongkui |
| contents | In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension dimension of both R itself and its degree-zero subring Re. Furthermore, we demonstrate that graded equivalence and graded separable equivalence preserve the extension dimension under appropriate conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The extension dimension of group graded rings Luo, Pei Liu, Zhongkui Category Theory 18G20, 16E10, 16W50, 16S50 In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension dimension of both R itself and its degree-zero subring Re. Furthermore, we demonstrate that graded equivalence and graded separable equivalence preserve the extension dimension under appropriate conditions. |
| title | The extension dimension of group graded rings |
| topic | Category Theory 18G20, 16E10, 16W50, 16S50 |
| url | https://arxiv.org/abs/2511.13255 |