On co-annihilators in residuated lattices

Abstract

In this paper, extension of relative co-annihilator in residuated lattices is introduced for subsets T and Y of residuated lattice L and is denoted by (T, Y). In this extension, T has a more important role than Y, as expected. It is proved if T is a filter, then co-annihilator of T relative to Y is a filter and is the same as the co-annihilator of T relative to the filter generated by Y. Also some theorems are stated and proved which determine the relationship between this special subset and the other types of filters. Finally, we give some conditions for subsets T and Y of residuated lattices L, for which (T, Y) is a special subset of L.