Semi-integral filters and semi-integral $BL$-algebras

In this paper, we introduced the concepts of semi-integral filters and semi-integral $BL$-algebras. With respect to these concepts, we give some related results. In particular, we give some relations among semi-integral $BL$-algebras, integral $BL$-algebras and local $BL$-algebra. Also, we give some relations among semi-integral filters and other types of filters in $BL$-algebras, such as prime, maximal, primary, perfect, normal, positive implicative and obstinate filters.