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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2010.02836 |
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| _version_ | 1866913194450092032 |
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| author | Atkarskaya, A. Kanel-Belov, A. Plotkin, E. Rips, E. |
| author_facet | Atkarskaya, A. Kanel-Belov, A. Plotkin, E. Rips, E. |
| contents | In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. We also provide a revision of a concept of Gröbner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_02836 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Group-like small cancellation theory for rings Atkarskaya, A. Kanel-Belov, A. Plotkin, E. Rips, E. Rings and Algebras Group Theory 20F67, 16S15, 16Z05 In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. We also provide a revision of a concept of Gröbner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem. |
| title | Group-like small cancellation theory for rings |
| topic | Rings and Algebras Group Theory 20F67, 16S15, 16Z05 |
| url | https://arxiv.org/abs/2010.02836 |