Non-generators in complete lattices and semilattices

DOI10.1007/S10474-022-01232-3arXiv2108.03303MaRDI QIDQ6374701

Paolo Lipparini

Publication date: 6 August 2021

Abstract: As well-known, in a finitary algebraic structure the set $Gamma$ of all the non-generators is the intersection of all the maximal proper substructures. In particular, $Gamma$ 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.

Mathematics Subject Classification ID

Complete lattices, completions (06B23) Semilattices (06A12)

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