Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures
Abstract
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations. The paper is divided into two parts. In the first part, we investigate the relationship between a pseudo MV-algebra with square root and its corresponding unital -group in the scene of two-divisibility. In the present second part, we find some conditions under which a particular class of pseudo MV-algebras can be embedded into pseudo MV-algebras with square roots. We introduce and investigate the concepts of a strict square root of a pseudo MV-algebra and a square root closure, and we compare both notions. We show that each MV-algebra has a square root closure. Finally, using the square root of individual elements of a pseudo MV-algebra, we find the greatest subalgebra of a special pseudo MV-algebra with weak square root.
Cite
@article{arxiv.2306.06114,
title = {Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures},
author = {Anatolij Dvurečenskij and Omid Zahiri},
journal= {arXiv preprint arXiv:2306.06114},
year = {2023}
}