The determinant of \(\lll\)-smooth semigroups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915346857852928 |
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| author | Shahzamanian, M. H. |
| author_facet | Shahzamanian, M. H. |
| contents | This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. We focus on a class of semigroups, called \( \lll \)-smooth semigroups, that allow meaningful structural analysis despite the absence of \( \ll \)-transitivity. Within this framework, we develop a method for computing contracted semigroup determinants, building on and extending the approach carried over from~\cite{Sha-Det2}. These computations are motivated by applications in coding theory, particularly by the potential extending the MacWilliams theorem for codes over semigroup algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The determinant of \(\lll\)-smooth semigroups Shahzamanian, M. H. Group Theory This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. We focus on a class of semigroups, called \( \lll \)-smooth semigroups, that allow meaningful structural analysis despite the absence of \( \ll \)-transitivity. Within this framework, we develop a method for computing contracted semigroup determinants, building on and extending the approach carried over from~\cite{Sha-Det2}. These computations are motivated by applications in coding theory, particularly by the potential extending the MacWilliams theorem for codes over semigroup algebras. |
| title | The determinant of \(\lll\)-smooth semigroups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2506.13700 |