We investigate ranges of ternary algebraic functions in lukasiewicz-Moisil algebras, where we give a characterization of algebraic functions whose ranges are intervals and we retrieve a canonical form of functions over three-element ternary lukasiewicz-Moisil algebras, a result due to Gr. C. Moisil, one of the founders of switching theory [Moi57]. In the second part of this paper we show that in a Noetherian or Artinian lattice distributivity and boundedness are implied by the condition that every algebraic functions has an interval as its range; this is actually a characterization of boundedness and distributivity in the class of lattices that have finite chains.
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机译：我们调查Lukasiewicz-Moisil代数中的三元代数功能的范围，在那里我们提供了代数函数的表征，其范围是间隔的，并且我们在三个元素三元Lukasiewicz-Moisil代数上检索规范形式的功能，这是由于GR引起的结果。 C. Moisil，切换理论的创始人之一[Moi57]。在本文的第二部分中，我们认为，在Neetherian或Artinian晶格分配和界限中，通过每个代数功能具有间隔的条件暗示;这实际上是具有有限链的格子类中的界限和分配的表征。
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