论文标题
在具有方形根的EMV代数上
On EMV-algebras with square roots
论文作者
论文摘要
平方根是一项具有特殊属性的单一操作。在论文中，我们介绍并研究了EMV-Elgebras的正方形根。首先，将在MV-Elgebras上定义的平方根的已知特性被概括为EMV-Elgebras，我们还为MV-Elgebras找到了一些新的。我们使用方形根来表征EMV-Elgebras。然后，我们发现EMV-Algebra的平方根与其代表具有顶部元素的EMV-Elgebra上的平方根之间的关系。我们表明，每个严格的EMV-Elgebra都有一个顶部元素，我们研究了具有特殊平方根的可划分的EMV-Elgebras和EMV-Elgebras之间的关系。最后，我们在部落，EMV部落上呈现了正方形的根源，并通过相应的Unital $ \ ell $ -group中的组加法呈现了MV-Algebra和EMV-Algebra上的任何平方根的完整表征。
A square root is a unary operation with some special properties. In the paper, we introduce and study square roots on EMV-algebras. First, the known properties of square roots defined on MV-algebras will be generalized for EMV-algebras, and we also find some new ones for MV-algebras. We use square roots to characterize EMV-algebras. Then, we find a relation between the square root of an EMV-algebra and the square root on its representing EMV-algebra with top element. We show that each strict EMV-algebra has a top element and we investigate the relation between divisible EMV-algebras and EMV-algebras with a special square root. Finally, we present square roots on tribes, EMV-tribes, and we present a complete characterization of any square root on an MV-algebra and on an EMV-algebra by group addition in the corresponding unital $\ell$-group.
