On medial Latin quandles and affine modules
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914315863326720 |
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| author | Ta, Luc |
| author_facet | Ta, Luc |
| contents | In this note, we show that the category of Latin (resp. commutative) medial quandles is equivalent to the category of affine modules over a certain Laurent polynomial ring (resp. the dyadic rationals). As applications, we describe free objects in these categories and obtain a structure theorem for finitely generated medial commutative quandles. We also characterize racks whose duals are commutative. Collectively, this solves two open problems of Bardakov and Elhamdadi (arXiv:2601.07057v2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On medial Latin quandles and affine modules Ta, Luc Group Theory Rings and Algebras Primary 20N02, 13C13, Secondary 08A05, 13C60, 57K12 In this note, we show that the category of Latin (resp. commutative) medial quandles is equivalent to the category of affine modules over a certain Laurent polynomial ring (resp. the dyadic rationals). As applications, we describe free objects in these categories and obtain a structure theorem for finitely generated medial commutative quandles. We also characterize racks whose duals are commutative. Collectively, this solves two open problems of Bardakov and Elhamdadi (arXiv:2601.07057v2). |
| title | On medial Latin quandles and affine modules |
| topic | Group Theory Rings and Algebras Primary 20N02, 13C13, Secondary 08A05, 13C60, 57K12 |
| url | https://arxiv.org/abs/2602.08875 |