GENERALIZED IDEALS WITH A TRIANGULAR NORM

The notion of generalized ideal is redefined with respect to a triangular norm for a completely distributive complete lattice with a greatest element and least element and the new mathematical object is termed as a T-g-ideal. We have furnished examples of T-g-ideals with different t-norms and shown that a T-g-ideal with respect to one tnorm may not be a T-g-ideal with respect to another t-norm. New T-g-ideals from old ones have been constructed through various poset operations like product of lattices, ordinal sum of lattices, dual of a lattice, interval of a lattice etc.