The determinant of \(\lll\)-smooth semigroups
Group Theory
2025-06-17 v1
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 -smooth semigroups, that allow meaningful structural analysis despite the absence of -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.
Cite
@article{arxiv.2506.13700,
title = {The determinant of \(\lll\)-smooth semigroups},
author = {M. H. Shahzamanian},
journal= {arXiv preprint arXiv:2506.13700},
year = {2025}
}