The determinant of $\lll$-smooth semigroups

M. H. Shahzamanian

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arXiv · 2506.13700

The determinant of $\lll$-smooth semigroups

M. H. Shahzamanian

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Abstract

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.

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BibTeX RIS

M. H. Shahzamanian. 2025-06-16. The determinant of $\lll$-smooth semigroups. https://arxiv.org/abs/2506.13700

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