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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Applied Logics

ISSN

2631-9810

e-ISSN

2631-9829

Svazek periodika

11

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

29

Strana od-do

"499 "- 527

Kód UT WoS článku

001308414500004

EID výsledku v databázi Scopus

2-s2.0-85202882686