Green’s relations for 2 × 2 matrices over linearly ordered abelian groups
We consider semigroups of 2 Ã 2 matrices over linearly ordered abelian groups with respect to multiplication, which is defined similarly to tropical algebra. We study Greenâs relations on such semigroups. In particular, we describe the R-, L- and H-classes of such semigroups and give a simple criter...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Estonian Academy Publishers
2025-02-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | https://kirj.ee/wp-content/plugins/kirj/pub/proc-1-2025-62-70_20250207125248.pdf |
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| Summary: | We consider semigroups of 2 Ã 2 matrices over linearly ordered abelian groups with respect to multiplication, which is defined similarly to tropical algebra. We study Greenâs relations on such semigroups. In particular, we describe the R-, L- and H-classes of such semigroups and give a simple criterion for determining whether two matrices are D-related. We prove that the D-relation coincides with the J-relation. We also study maximal subgroups of such semigroups. It turns out that if the abelian group is divisible, then these maximal subgroups can have two different forms. |
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| ISSN: | 1736-6046 1736-7530 |