Document Type : Original Manuscript


1 Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar Abbas, Iran.

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


‎In this paper‎, ‎the concepts of weakly prime filters and super-max filters in $\mathrm{BL}$-algebras are introduced‎, ‎and the relationships between them are discussed‎. ‎Also‎, ‎some properties and relations between these filters and other types of filters in $\mathrm{BL}$-algebras are given‎. ‎With some examples‎, ‎it is shown that these filters have differences‎. ‎After that‎, ‎the notions of weakly linear $\mathrm{BL}$-algebras and weak top $\mathrm{BL}$-algebras are defined and investigated‎. ‎Finally‎, ‎using the notion of a weakly prime filter‎, ‎a new topology on $\mathrm{BL}$-algebras is defined and studied‎.


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