[See also Stern-Brocot.]
--------------------------------------------------
A. Clifford: Matrix representations of completely simple semigroups.
Am. J. Math. 64 (1942), 327-342.

3353 A. Clifford/G. Preston: The algebraic theory of semigroups.
2 volumes. AMS 1961. 

21069 Olexandr Ganyushkin/Volodymyr Mazorchuk/Benjamin Steinberg:
On the irreducible representations of a finite semigroup.
Proc. AMS ... (2009), 8p.

Edwin Hewitt/H. Zuckerman: Finite-dimensional convolution algebras.
Acta Math. 93 (1955), 67-119.

Edwin Hewitt/H. Zuckerman: The irreducible representations of a
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24248 David Jackson: Decision and separability problems for Baumslag-Solitar
semigroups. Int. J. Algebra Comp. 12 (2002), 33-49.

W. Munn: On semigroup algebras. Proc. Camb. Phil. Soc. 51 (1955), 1-15.

W. Munn: Matrix representations of semigroups.
Proc. Camb. Phil. Soc. 53 (1957), 5-12.

W. Munn: The characters of the symmetric inverse semigroup.
Proc. Camb. Phil. Soc. 53 (1957), 13-18.

W. Munn: Irreducible matrix representations of semigroups.
Quart. J. Math. Oxford 11 (1960), 295-309.

I. Ponizovski: On matrichnykh predstavleniyakh assotsiativnykh sistem.
Mat. Sb. 38 (1956), 241-260.

I. Ponizovski: O matrichnykh neprivodimykh predstavleniyakh konechnykh
polugrupp. Usp. Mat. Nauk 13 (1958), 139-144.

G. Preston: Matrix representations of semigroups.
Quart. J. Math. Oxford 9 (1958), 169-176.