%0 Journal Article %T RADICAL OF FILTERS IN RESIDUATED LATTICES %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Motamed, S. %D 2017 %\ 01/01/2017 %V 4 %N 2 %P 111-121 %! RADICAL OF FILTERS IN RESIDUATED LATTICES %K ‎(Maximal) Prime filter‎ %K ‎Radical‎ %K ‎Residuated‎ ‎lattice %R 10.22044/jas.2017.852 %X ‌In this paper‌, ‌the notion of the radical of a filter in‌ ‌residuated lattices is defined and several characterizations of‌ ‌the radical of a filter are given‌. ‌We show that if F is a‌ ‌positive implicative filter (or obstinate filter)‌, ‌then‌ ‌Rad(F)=F‌. ‌We proved the extension theorem for radical of filters in residuated lattices‌. ‌Also‌, ‌we study the radical‌ ‌of filters in linearly ordered residuated lattices‌. %U https://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf