Decidability of theories of modules over tubular algebras
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866910754290008064 |
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| author | Gregory, Lorna |
| author_facet | Gregory, Lorna |
| contents | We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra (over a recursively given field) is tame if and only its common theory of modules is decidable. Moreover, as a corollary, we are able to confirm this conjecture for the class of concealed canonical algebras over algebraically closed fields. These are the first examples of non-domestic algebras which have been shown to have decidable theory of modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1603_03284 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Decidability of theories of modules over tubular algebras Gregory, Lorna Logic Representation Theory 03C60, 16G60, 03D35, 16G60, 16D90 We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra (over a recursively given field) is tame if and only its common theory of modules is decidable. Moreover, as a corollary, we are able to confirm this conjecture for the class of concealed canonical algebras over algebraically closed fields. These are the first examples of non-domestic algebras which have been shown to have decidable theory of modules. |
| title | Decidability of theories of modules over tubular algebras |
| topic | Logic Representation Theory 03C60, 16G60, 03D35, 16G60, 16D90 |
| url | https://arxiv.org/abs/1603.03284 |