As is 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.
Lipparini, P. (2022). Non-generators in complete lattices and semilattices. ACTA MATHEMATICA HUNGARICA [10.1007/s10474-022-01232-3].
Non-generators in complete lattices and semilattices
Lipparini, P.
2022-01-01
Abstract
As is 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.File in questo prodotto:
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