On co-annihilators in residuated lattices
Farnaz Ghanavizi Maroof, Arsham Borumand Saeid, Esfandiar Eslami · Journal of Intelligent & Fuzzy Systems · 2016
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 .