Nearlattices

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. Key words: Nearlattice; semilattice; ideal; congruence; distributivity; modularity; 0-distributivity; annihilator. 2000 Mathematics Subject Classification: 06A12, 06D99, 06C99

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Ivan Chajda, Miroslav Kolarík
• Keywords: Certain Properties, DM 2008, Principal Filter, Semilattice Order