The purpose of this paper is to begin studying the computation of the nonzero determinant of semigroups within the class of finite semigroups that possesses a pair of non-commutative idempotents. This paper focuses on a class of these semigroups introduced as $\ll$-smooth semigroups. This computation is applicable in the context of the extension of the MacWilliams theorem for codes over semigroup algebras.
An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata
The q-theory of finite semigroups: history and mathematics
The determinant of finite semigroups of the pseudovariety ECOM
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