Decomposition techniques for finite semigroups, using categories. I
A surjective morphism of semigroups \(\theta\) : \(S\to T\) is said to be a maximal proper surmorphism if \(\theta\) is not an isomorphism and, for any factorization \(\theta =\theta_ 1\theta_ 2\), one the factors \(\theta_ 1\) and \(\theta_ 2\) is an isomorphism. The paper presents a refinement of the classification of maximal proper surmorphisms of finite semigroups obtained by \textit{J. Rhodes} [Math. Syst. Theory 1, 289-304 (1967; Zbl 0204.033)].
classification of maximal proper surmorphisms
scientific article; zbMATH DE number 4120425