International Mathematical Forum, 5, 2010, no. 57, 2809 - 2816 Stabilizer in BL-Algebras and its Properties Masoud Haveshki 1 and Mahboobeh Mohamadhasani Department of Mathematics, Hormozgan University P.O. Box 3995, Bandarabbas, Iran m.Haveshki@Hormozgan.ac.ir m.Mohamadhasani@Hormozgan.ac.ir Abstract In this paper we introduce stabilizer of X and stabilizer of X with respect to Y , for subsets X and Y of A. We show that stabilizer X is a filter and also stabilizer of X with respect to Y is a filter . Then we study some properties of them. Mathematics Subject Classification: 06F35, 03G25 Keywords: BL-algebra, filter, stabilizer 1 Introduction BL- algebras were invented by P. Hajek [3] in order to provide an algebraic proof of the completeness theorem of ”Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The language of propositional Hajek Basic Logic [3] contains the binary connective o and ⇒ , the constant ¯ 0 . Axioms of BL are: (A1) (ϕ ⇒ ψ) ⇒ ((ψ ⇒ ω) ⇒ (ϕ ⇒ ω)), (A2) (ϕoψ) ⇒ ϕ, (A3) (ϕoψ) ⇒ (ψoϕ), (A4) (ϕo(ϕ ⇒ ψ)) ⇒ (ψo(ψ ⇒ ϕ)), (A5a) (ϕ ⇒ (ψ ⇒ ω)) ⇒ ((ϕoψ) ⇒ ω), (A5b) ((ϕoψ) ⇒ ω) ⇒ (ϕ ⇒ (ψ ⇒ ω)), 1 m.haveshki@hormozgan.ac.ir