n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

Dvurecenskij A.; Lachman D.

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n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

机译：n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

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? 2021 Elsevier B.V.This article is a continuation of our research on a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on lexicographic types of quantum structures which started in Dvure?enskij and Lachman (https://doi.org/10.1016/j.fss.2021.05.005). There we presented the main properties of n-dimensional spectral resolutions and observables, and we studied in depth characteristic points which are crucial for our study. Here we present the main body of our research. We investigate a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions with values in a lexicographic form of quantum structures such as 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 of spectral resolutions we have more characteristic points. The results obtained are applied to the existence of an n-dimensional meet joint observable of n one-dimensional observables on a perfect MV-algebra and a sum of n-dimensional observables.

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《Fuzzy sets and systems》 |2022年第15期|17-42|共26页
作者
Dvurecenskij A.; Lachman D.;
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作者单位

Mathematical Institute Slovak Academy of SciencesMathematical Institute Slovak Academy of Sciences||Department of Algebra and Geometry Palacky University Olomouc;

||Department of Algebra and Geometry Palacky University Olomouc;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
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Characteristic point; Interpolation; Joint observable; k-perfect effect algebra; k-perfect MV-algebra; Lexicographic MV-algebra; n-dimensional observable; n-dimensional spectral resolution; Sum of observables; Unital partially ordered group;

n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

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