Abstract
All irreducible representations of the Chinese monoid Cn, of any rank n, over a nondenumerable algebraically closed field K, are constructed. It turns out that they have a remarkably simple form and they can be built inductively from irreducible representations of the monoid C2. The proof shows also that every such representation is monomial. Since Cn embeds into the algebra K[Cn]/J(K[Cn]), where J(K[Cn]) denotes the Jacobson radical of the monoid algebra K[Cn], a new representation of Cn as a subdirect product of the images of Cn in the endomorphism algebras of the constructed simple modules follows.
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