The Krohn-Rhodes Theorem and Local Divisors

Details The Krohn-Rhodes Theorem and Local Divisors The Krohn-Rhodes Theorem and Local Divisors

2011-11-07

arxiv.org/abs/1111.1585v1

Mathematics

Group Theory

Scientific paper

We give a new proof of the Krohn-Rhodes Theorem using local divisors. The
proof provides nearly as good a decomposition in terms of size as the holonomy
decomposition of Eilenberg, avoids induction on the size of the state set, and
works exclusively with monoids with the base case of the induction being that
of a group.

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