Abstract. They are studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also it's done some more general lattice theory research. There are posed several open problems. Detailed study of filters is required for my ongoing research which will be published as ``Algebraic General Topology'' series.

Received: October 11, 2011

AMS Subject Classification: 54A20, 06A06, 06B99

Key Words and Phrases: filters, ideals, lattice of filters, pseudodifference, pseudocomplement

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