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Regular and Boolean elements in hoops and constructing Boolean algebras using regular filtersopen access
- Authors
- Aaly, Kologani M.; Jun, Y.B.; Borzooei, R.A.
- Issue Date
- Mar-2023
- Publisher
- Sciendo
- Keywords
- archimedean hoop; Boolean algebra; Boolean element; Hoop; regular element; regular filter; Stone algebra
- Citation
- Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, v.31, no.2, pp 5 - 22
- Pages
- 18
- Indexed
- SCIE
SCOPUS
- Volume
- 31
- Number
- 2
- Start Page
- 5
- End Page
- 22
- ISSN
- 1224-1784
1844-0835
- 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. © 2023 M. Aaly Kologani et al., published by Sciendo.
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