on semi maximal filters in bl-algebras

In this paper, rst we study the semi maximal lters in linear bl-algebras and we prove that any semi maximal lter is a primary lter. then, we investigate the radical of semi maximal lters in bl-algebras. moreover, we determine the relationship between this lters and other types of lters in bl-algebras and godel algebra. specially, we prove that in a godel algebra, any fantastic lter is a semi maximal lter and any semi maximal lter is an (n-fold) positive implicative lter. also, in a bl-algebra, any semi maximal and implicative lter is a positive implicative lter. finally, we give an answer to the open problem in [s. motamed, l. torkzadeh, a. borumand saeid and n. mohtashamnia, radical of lters in bl-algebras, math. log. quart. 57, no. 2, (2011), 166-179 ]