Congruence-simple matrix semirings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929361186193408 |
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| author | Kala, Vítězslav Kepka, Tomáš Korbelář, Miroslav |
| author_facet | Kala, Vítězslav Kepka, Tomáš Korbelář, Miroslav |
| contents | It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a semiring $S$, is congruence-simple, provided that either $S$ has a multiplicatively absorbing element or $S$ is commutative and additively cancellative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06921 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Congruence-simple matrix semirings Kala, Vítězslav Kepka, Tomáš Korbelář, Miroslav Rings and Algebras 06A12, 16Y60, 20M14 It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a semiring $S$, is congruence-simple, provided that either $S$ has a multiplicatively absorbing element or $S$ is commutative and additively cancellative. |
| title | Congruence-simple matrix semirings |
| topic | Rings and Algebras 06A12, 16Y60, 20M14 |
| url | https://arxiv.org/abs/2303.06921 |