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arXiv · 2108.03303

Non-generators in complete lattices and semilattices

Paolo Lipparini
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Abstract

As well-known, in a finitary algebraic structure the set $Γ$ of all the non-generators is the intersection of all the maximal proper substructures. In particular, $Γ$ is a substructure. We show that the corresponding statements hold for complete semilattices but fail for complete lattices, when as the notion of substructure we take complete subsemilattices and complete sublattices, respectively.

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Paolo Lipparini. 2022-01-02. Non-generators in complete lattices and semilattices. https://doi.org/10.1007/s10474-022-01232-3

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