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Ideals, congruences and annihilators on nearlattices

Ivan Chajda, Miroslav Kolařík (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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