<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We study hoops in order to give some new characterizations for regular and Boolean elements in hoops and we study the relationship between them. Specially, we prove that any bounded <underline>v</underline>-hoop is a Stone algebra if and only if <italic>MV</italic> -center set and Boolean elements set are equal. Then we define the concept of regular filter in hoops and <underline>v</underline>-hoops with RF-property and peruse some properties of them. In addition, we show that each <underline>v</underline>-hoop with RF-property, is a Boolean algebra and any hoop <italic>A</italic> with RF-property such that <italic>B</italic>(<italic>A</italic>) = {0, 1}, is a local hoop. Finally, we prove that any hoop <italic>A</italic> has RF-property if and only if <italic>Spec</italic>(<italic>A</italic>) = <italic>Max</italic>(<italic>A</italic>) and if and only if <italic>A</italic> is a hyperarchimedean.</p>
</abstract>

We study hoops in order to give some new characterizations for regular and Boolean elements in hoops and we study the relationship between them. Specially, we prove that any bounded v-hoop is a Stone algebra if and only if MV -center set and Boolean elements set are equal. Then we define the concept of regular filter in hoops and v-hoops with RF-property and peruse some properties of them. In addition, we show that each v-hoop with RF-property, is a Boolean algebra and any hoop A with RF-property such that B(A) = {0, 1}, is a local hoop. Finally, we prove that any hoop A has RF-property if and only if Spec(A) = Max(A) and if and only if A is a hyperarchimedean.

Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters

Department of Mathematics, Faculty of Mathematical Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We study hoops in order to give some new characterizations for regular and Boolean elements in hoops and we study the relationship between them. Specially, we...

Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters

Published Online: Mar 27, 2023

Page range: 5 - 22

Received: Jul 20, 2022

Accepted: Nov 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0016

Keywords
Hoop, Boolean element, regular element, regular filter, Stone algebra, Boolean algebra, archimedean hoop

© 2023 M. Aaly Kologani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters

Published Online: Mar 27, 2023

Page range: 5 - 22

Received: Jul 20, 2022

Accepted: Nov 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0016

KeywordsHoop, Boolean element, regular element, regular filter, Stone algebra, Boolean algebra, archimedean hoop

© 2023 M. Aaly Kologani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Hoop, Boolean element, regular element, regular filter, Stone algebra, Boolean algebra, archimedean hoop