QUASI-VALUATION MAPS BASED ON SUBALGEBRA AND IDEAL CONCEPT IN BM-ALGEBRA

J. Thomas and K. Indhira

  DOI:  https://doi.org/10.37418/amsj.9.11.110

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The notion of SQV-map and IQV-map in a BM-algebra are introduced and the relation between them are studied. Using these notions, the binary operation in BM-algebra is found to be uniformly continuous by constructing (pseudo) metric spaces. A quotient BM-algebra is constructed using the congruence relation induced by the IQV-map on it. The relation between the induced congruence relation and an ideal obtained from an IQV-map are studied. The condition under which two BM-algebras become homeomorphic is also derived by defining suitable IQV-maps on them.

Keywords: BM-algebra, quasi-valuation maps, quotient BM-algebra, pseudo-metric, isometry, homeomorphism.