Indecomposable Injectives over the Jacobson Algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909342245060608 |
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| author | Colpi, Riccardo Mantese, Francesca Tonolo, Alberto |
| author_facet | Colpi, Riccardo Mantese, Francesca Tonolo, Alberto |
| contents | Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K<X,Y | XY = 1>, i.e., the free associative K-algebra on two (noncommuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the charaterization of the injective envelope of the simple modules over K<X, Y | XY = 1>. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_05790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Indecomposable Injectives over the Jacobson Algebra Colpi, Riccardo Mantese, Francesca Tonolo, Alberto Rings and Algebras 16S88, 16S99 Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K<X,Y | XY = 1>, i.e., the free associative K-algebra on two (noncommuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the charaterization of the injective envelope of the simple modules over K<X, Y | XY = 1>. |
| title | Indecomposable Injectives over the Jacobson Algebra |
| topic | Rings and Algebras 16S88, 16S99 |
| url | https://arxiv.org/abs/2410.05790 |