Abstract: We introduce some particular classes of filters and order-ideals in distributive semilattices, called \alpha-filters and \alpha-order-ideals, respectively. In particular, we study \alpha-filters and \alpha-order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through \alpha-order-ideals.
Keywords: bounded distributive semilattice; quasicomplement; relative annihilator; order-ideal; filter
DOI: DOI 10.14712/1213-7243.2021.004
AMS Subject Classification: 06A12 03G10