Rigidity of Graded Integral Domains and of their Veronese Subrings
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917891690987520 |
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| author | Daigle, Daniel |
| author_facet | Daigle, Daniel |
| contents | A ring R is said to be rigid if the only locally nilpotent derivation of R is the zero derivation. Let G be an abelian group, and B = (direct sum of B_i for i in G) be a G-graded commutative integral domain of characteristic 0. For each subgroup H of G, consider the Veronese subring B(H) of B, defined by B(H) = (direct sum of the B_i for i in H). We study the following questions. If B is non-rigid, does it follow that B(H) is non-rigid? Can derivations of B(H) be extended to derivations of B? What are the properties of the set of subgroups H of G such that B(H) is non-rigid? |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_05066 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of Graded Integral Domains and of their Veronese Subrings Daigle, Daniel Commutative Algebra Algebraic Geometry Primary: 13N15, 14R20. Secondary: 14C20, 14R05, 14R25 A ring R is said to be rigid if the only locally nilpotent derivation of R is the zero derivation. Let G be an abelian group, and B = (direct sum of B_i for i in G) be a G-graded commutative integral domain of characteristic 0. For each subgroup H of G, consider the Veronese subring B(H) of B, defined by B(H) = (direct sum of the B_i for i in H). We study the following questions. If B is non-rigid, does it follow that B(H) is non-rigid? Can derivations of B(H) be extended to derivations of B? What are the properties of the set of subgroups H of G such that B(H) is non-rigid? |
| title | Rigidity of Graded Integral Domains and of their Veronese Subrings |
| topic | Commutative Algebra Algebraic Geometry Primary: 13N15, 14R20. Secondary: 14C20, 14R05, 14R25 |
| url | https://arxiv.org/abs/2308.05066 |