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Keywords:
nearlattice; semilattice; ideal; congruence; distributivity; modularity; $0$-distributivity; annihilator
nearlattice; semilattice; ideal; congruence; distributivity; modularity; $0$-distributivity; annihilator
Summary:
By a nearlattice is meant a join-semilattice having the property that every principal filter is a lattice with respect to the semilattice order. We introduce the concept of (relative) annihilator of a nearlattice and characterize some properties like distributivity, modularity or $0$-distributivity of nearlattices by means of certain properties of annihilators.
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