Abstract 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.

中文翻译：

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通过推导研究 MV-代数

摘要 本文的主要目标是在推导方面给出 MV-代数的一些表示。在本文中，我们研究了隐含和差分推导的一些性质，并给出了它们在 MV 代数中的特征。然后，我们证明每个布尔代数（幂等 MV-代数）与所有蕴涵推导的代数同构，并通过蕴涵推导获得 MV-代数的直接乘积表示。此外，我们证明了 MV 代数上的正则蕴涵和差分推导是一一对应的，并证明了正则推导对 (d, g) 和伽罗瓦连接之间的关系，其中 d 和 g 是正则差分和蕴涵推导分别在 L 上。最后，