Geodesic
Matrix representations of semigroups
Glasgow mathematical journal, Tome 8 (1967) no. 1, pp. 1-13

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In a series of papers [6], [7], [8], [10], Munn has considered the problem of constructing all irreducible representations of a semigroup by matrices over a field. In [10], he showed how to construct all the irreducible representations of an arbitrary inverse semigroup from those of associated Brandt semigroups. In this paper, we generalize the method of [10] to give a construction for the irreducible representations of an arbitrary semigroup from those of certain associated semigroups 
McAlister, D. B. Matrix representations of semigroups. Glasgow mathematical journal, Tome 8 (1967) no. 1, pp. 1-13. doi: 10.1017/S0017089500000033
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