Idempotent Residuated Lattices and psG-filters
Xiaohong Zhang · Mohu xitong yu shuxue · 2011
This paper is concerned with a special residuated lattice — idempotent residuated lattice,and it is proved that if a general residuated lattice is idempotent then it is commutative residuated lattice,in other words,non-commutative residuated lattice does not exist.The basic properties of idempotent residuated lattices are studied and the relation of several special residuated lattices are discussed.Moreover,in general residuated lattice the concept of psG-filter is introduced and some equivalence conditions are given.Based on these results,idempotent residuated lattice is characterized by psG-filters.