Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analele Universitatii Ovidius Constanta - Seria Matematica de Gruyter

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

Loading next page...
 
/lp/de-gruyter/regular-and-boolean-elements-in-hoops-and-constructing-boolean-KILY2tcBxO

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2023 M. Aaly Kologani et al., published by Sciendo
eISSN
1844-0835
DOI
10.2478/auom-2023-0016
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Analele Universitatii Ovidius Constanta - Seria Matematicade Gruyter

Published: Mar 1, 2023

Keywords: Hoop; Boolean element; regular element; regular filter; Stone algebra; Boolean algebra; archimedean hoop; Primary 03G10, 06B99; Secondary 06B75

There are no references for this article.