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A note on generators of the endomorphism semigroup of an infinite countable chain

    https://doi.org/10.1142/S0219498817500311Cited by:6 (Source: Crossref)

    In this note, we consider the semigroup 𝒪(X) of all order endomorphisms of an infinite chain X and the subset J of 𝒪(X) of all transformations α such that |Im(α)|=|X|. For an infinite countable chain X, we give a necessary and sufficient condition on X for 𝒪(X)=J to hold. We also present a sufficient condition on X for 𝒪(X)=J to hold, for an arbitrary infinite chain X.

    Communicated by L. Bokut

    AMSC: 20M20, 20M10

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