Study of MV-algebras via derivations

The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair ( d, g ) and the Galois connection, where d and g are regular difference and implicative derivation on L , respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.

Abstract licence: CC BY-NC-ND

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