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The semiring of 1-preserving endomorphisms of a semilattice

Jaroslav Ježek, Tomáš Kepka (2009)

Czechoslovak Mathematical Journal

We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.

α -filters and α -order-ideals in distributive quasicomplemented semilattices

Ismael Calomino, Sergio A. Celani (2021)

Commentationes Mathematicae Universitatis Carolinae

We introduce some particular classes of filters and order-ideals in distributive semilattices, called α -filters and α -order-ideals, respectively. In particular, we study α -filters and α -order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through α -order-ideals.

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