Titlebook: Representation Theory of Finite Monoids; Benjamin Steinberg Textbook 2016 Springer International Publishing Switzerland 2016 automata theo

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9 The Representation Theory of Inverse Monoidsd M?bius inversion. In fact, this work has a precursor in the work of Rukola?ne?[Ruk78, Ruk80], who used alternating sums of idempotents to achieve the same effect as M?bius inversion and used Brandt inverse semigroups instead of groupoids. The author only became aware of the work of Rukola?ne after

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13 Transformation Monoids role in automata theory and we provide here some applications in this direction. In particular, we study connections with the popular ?erny conjecture?[?64]; see?[Vol08] for a survey. This chapter is primarily based upon the paper?[Ste10b].

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2 ,-trivial Monoidss and prime ideals of arbitrary finite monoids, as they shall play an important role in both the general theory and in the structure theory of .-trivial monoids. The second section concerns .-trivial monoids and, in particular, left regular bands, which are precisely the regular .-trivial monoids.

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