Document Type: Original Manuscript

Author

Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.

Abstract

‎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.

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