Affiliations: [a] Department of Mathematics, Shahid Beheshti University, Tehran, Iran
| [b] Research Institute for Natural Sciences, Dept. of Mathematics, Hanyang University, Seoul, Korea
| [c] Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Correspondence:
[*]
Corresponding author. H.S. Kim, Department of Mathematics, Hanyang University, Seoul, Korea. Tel.: +82 2 2290 0897. Fax: +82 2 2281 0019; E-mail: heekim@hanyang.ac.kr.
Abstract: 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
U
and
V
on A and on A/F respectively such that
(A,U)
and
(A/F,V)
are (semi)topological BL-algebras.
Keywords: (Semi)topological BL-algebra, prenorm, norm, premetric, metric space
