Splitting criteria for projective modules over polynomial algebras
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909963398414336 |
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| author | Banerjee, Sourjya Das, Mrinal Kanti |
| author_facet | Banerjee, Sourjya Das, Mrinal Kanti |
| contents | This article investigates the splitting problem for finitely generated projective modules $P$ over affine algebras over algebraically closed fields and their polynomial extensions. We then address an open question due to M. Roitman on monic inversion principle for projective modules and prove it in the affirmative for finitely generated rings. For affine algebras over $\overline{\mathbb{F}}_p$, we prove a monic inversion principle for ideals. We also exhibit some applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_06819 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Splitting criteria for projective modules over polynomial algebras Banerjee, Sourjya Das, Mrinal Kanti Commutative Algebra 13C10, 19A13, 19A15 This article investigates the splitting problem for finitely generated projective modules $P$ over affine algebras over algebraically closed fields and their polynomial extensions. We then address an open question due to M. Roitman on monic inversion principle for projective modules and prove it in the affirmative for finitely generated rings. For affine algebras over $\overline{\mathbb{F}}_p$, we prove a monic inversion principle for ideals. We also exhibit some applications. |
| title | Splitting criteria for projective modules over polynomial algebras |
| topic | Commutative Algebra 13C10, 19A13, 19A15 |
| url | https://arxiv.org/abs/2206.06819 |