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

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 -hoop is a Stone algebra if and only if -center set and Boolean elements set are equal. Then we define the concept of...

Full description

Saved in:
Bibliographic Details
Published inAnalele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Vol. 31; no. 2; pp. 5 - 22
Main Authors Aaly Kologani, M., Jun, Y.B., Borzooei, R.A.
Format Journal Article
LanguageEnglish
Published Sciendo 01.03.2023
Subjects
archimedean hoop
Boolean algebra
Boolean element
Hoop
Primary 03G10, 06B99
regular element
regular filter
Secondary 06B75
Stone algebra
Online AccessGet full text

Cover

More Information
Summary: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 -hoop is a Stone algebra if and only if -center set and Boolean elements set are equal. Then we define the concept of regular filter in hoops and -hoops with RF-property and peruse some properties of them. In addition, we show that each -hoop with RF-property, is a Boolean algebra and any hoop with RF-property such that ) = {0, 1}, is a local hoop. Finally, we prove that any hoop has RF-property if and only if ) = ) and if and only if is a hyperarchimedean.
ISSN:1844-0835
DOI:10.2478/auom-2023-0016