WEAK CLOSURE OPERATIONS WITH SPECIAL TYPES IN LOWER BCK-SEMILATTICES

Abstract

The notions of (strong) quasi prime mapping on the set of all ideals, t-type weak closure operation, and tender (resp., naive, sheer, feeble tender) weak closure operation are introduced, and their relations and properties are investigated.  Conditions for a weak closure operation to be of t-type are provided.  Given a weak closure operation, conditions for the new weak closure operation to be of t-type and to be a naive (sheer, feeble tender) weak closure operation are considered.  We show that the new weak closure operation is the smallest tender weak closure operation containing the given weak closure operation.