Abstract Closure operations on posets have been investigated and applied extensively to lattices of congruences of various algebraic structures. In this paper, we initiate the study of closure operations on MV-algebras and star operations on MV-modules. The connections between closure (star) operations studied here and those of semirings as well as those of lattice-ordered rings are also investigated. We provide several examples of these closure operations and star operations and also study some of their main properties.

中文翻译：

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MV-代数的闭运算

摘要 对偏序集的闭运算已被研究并广泛应用于各种代数结构的同余格。在本文中，我们开始研究 MV 代数上的闭包运算和 MV 模块上的星型运算。还研究了此处研究的闭合（星形）运算与半环以及晶格有序环的闭合（星形）运算之间的联系。我们提供了这些闭包操作和星形操作的几个示例，并研究了它们的一些主要属性。