Semi Maximal Filters on Pseudo MTL-algebras

Pseudo MTL-algebras or weak pseudo BL-algebras are a non commutative structures arise from pseudo t-norms pseudoBl-algebras without the pseudo divisibility condition. In this paper, we introduce the notion of semi maximal filters inpseudo MTL-algebras and prove any semi-monad filter is a primary filter in pseudo MTL-algebras. Also, we studyradical of a filter in integral pseudo MTL-algebras and we will extract important results and relationships