In this paper we define the notions of a norm and a prenorm on BL-algebras and we give some methods for constructing them. We introduce (pre)metrics on BL-algebras and find some connections between them and (pre)norms. Using prenorms, we find some conditions that a BL-algebra become a metric space. Finally, we show that if there exists a prenorm on a BL-algebra A, then for any filter F in A, there are topologies and on A and on A/F respectively such that and are (semi)topological BL-algebras.
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