Relative Faithful Exact Functors and Their Applications to Homological Modules
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915825784455168 |
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| author | Zhang, Xiaolei Qiao, Lei Kim, Hwankoo |
| author_facet | Zhang, Xiaolei Qiao, Lei Kim, Hwankoo |
| contents | The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and exact--play fundamental roles across various areas of algebra. In this paper, we extend these notions to the setting of $w$-operation theory. By introducing the concept of $w$-faithfully exact functors, we define and investigate the notions of $w$-faithfully projective, $w$-faithfully flat, and $w$-faithfully injective modules. We establish their fundamental properties and demonstrate their effectiveness in generalizing classical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relative Faithful Exact Functors and Their Applications to Homological Modules Zhang, Xiaolei Qiao, Lei Kim, Hwankoo Commutative Algebra The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and exact--play fundamental roles across various areas of algebra. In this paper, we extend these notions to the setting of $w$-operation theory. By introducing the concept of $w$-faithfully exact functors, we define and investigate the notions of $w$-faithfully projective, $w$-faithfully flat, and $w$-faithfully injective modules. We establish their fundamental properties and demonstrate their effectiveness in generalizing classical results. |
| title | Relative Faithful Exact Functors and Their Applications to Homological Modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2603.00970 |