Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627587" target="_blank" >RIV/61989592:15310/24:73627587 - isvavai.cz</a>

Result on the web

<a href="https://arxiv.org/abs/2306.04623" target="_blank" >https://arxiv.org/abs/2306.04623</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.48550/arXiv.2306.04623" target="_blank" >10.48550/arXiv.2306.04623</a>

Result language

angličtina

Original language name

Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots

Original language description

In [17], we started the investigation of pseudo MV-algebras with square roots. In the present paper, we 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 present first part, we investigate the relationship between a pseudo MV-algebra with square root and its corresponding unital &amp; ell;-group in the scene of two-divisibility. We characterize strict and non-strict square roots and we describe square roots on strongly(H,1)-perfect pseudo MV-algebras. In the 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 investigate the concepts of a strict square root closure and a square root closure of a pseudo MV-algebra, 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 roots.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Applied Logics

ISSN

2631-9810

e-ISSN

2631-9829

Volume of the periodical

11

Issue of the periodical within the volume

4

Country of publishing house

GB - UNITED KINGDOM

Number of pages

29

Pages from-to

"499 "- 527

UT code for WoS article

001308414500004

EID of the result in the Scopus database

2-s2.0-85202882686