论文标题
$ n $二维可观察到$ k $ - 完美的MV-Elgebras和$ k $ - 完美的效应代数。 I.特征点
$n$-dimensional Observables on $k$-Perfect MV-Algebras and $k$-Perfect Effect Algebras. I. Characteristic Points
论文作者
论文摘要
在本文中，我们研究了$ n $维的可观测值和$ n $维光谱分辨率之间的一对一对应关系，其值是一种词典形式的量子结构，例如完美的MV-Elgebras或Perfect效应代数。该问题的多维版本比一维的版本更为复杂，因为如果我们的代数结构为$ k $ $ k> 1 $，那么即使对于二维情况，我们也有更多特征点。所获得的结果还适用于存在$ n $ n $维的联合观察到完美的MV-Algebra上的一维观测值。结果分为两个部分。在第一部分中，我们介绍了$ n $二维可观测值和$ n $二维光谱分辨率，并在词典类型效应代数和词典MV-Elgebras上进行重音。我们专注于光谱分辨率的特征点，而主体则是在第二部分中，其中显示了可观察到的分辨率与光谱分辨率之间的一对一关系。
In the paper, we investigate a one-to-one correspondence between $n$-dimensional observables and $n$-dimensional spectral resolutions with values in a kind of a lexicographic form of quantum structures like perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is $k$-perfect for $k>1$, then even for the two-dimensional case we have more characteristic points. The obtained results are also applied to existence of an $n$-dimensional meet joint observable of $n$ one-dimensional observables on a perfect MV-algebra. The results are divided into two parts. In Part I, we present notions of $n$-dimensional observables and $n$-dimensional spectral resolutions with accent on lexicographic type effect algebras and lexicographic MV-algebras. We concentrate on characteristic points of spectral resolutions and the main body is in Part II where one-to-one relations between observables and spectral resolutions are presented.
