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 v-hoop is a Stone algebra if and only if MV -center set and Boolean elements set are equal. Then we define the concept...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2023-03-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2023-0016 |
| _version_ | 1797848584765308928 |
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| author | Aaly Kologani M. Jun Y.B. Borzooei R.A. |
| author_facet | Aaly Kologani M. Jun Y.B. Borzooei R.A. |
| author_sort | Aaly Kologani M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T18:29:45Z |
| format | Article |
| id | doaj.art-6320b0d908944d1787990234d373169a |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-09T18:29:45Z |
| publishDate | 2023-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-6320b0d908944d1787990234d373169a2023-04-11T17:19:08ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352023-03-0131252210.2478/auom-2023-0016Regular and Boolean elements in hoops and constructing Boolean algebras using regular filtersAaly Kologani M.0Jun Y.B.1Borzooei R.A.21Hatef Higher Education Institute, Zahedan, Iran2Department of Mathematics Education, Gyeongsang National University, Jinju52828, Korea3Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranWe 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.https://doi.org/10.2478/auom-2023-0016hoopboolean elementregular elementregular filterstone algebraboolean algebraarchimedean hoopprimary 03g10, 06b99secondary 06b75 |
| spellingShingle | Aaly Kologani M. Jun Y.B. Borzooei R.A. Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica hoop boolean element regular element regular filter stone algebra boolean algebra archimedean hoop primary 03g10, 06b99 secondary 06b75 |
| title | Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters |
| title_full | Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters |
| title_fullStr | Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters |
| title_full_unstemmed | Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters |
| title_short | Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters |
| title_sort | regular and boolean elements in hoops and constructing boolean algebras using regular filters |
| topic | hoop boolean element regular element regular filter stone algebra boolean algebra archimedean hoop primary 03g10, 06b99 secondary 06b75 |
| url | https://doi.org/10.2478/auom-2023-0016 |
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