Boolean Rings Based On Multirings
The purpose of this paper is to construct Boolean rings from multirings. In this regards, a method to construct a multigroup(multiring) on a given non-empty set, are introduced and its properties has been investigated. Also, an equivalence relation on a multiring are introduced and it is extended to...
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| Format: | Article |
| Language: | English |
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University of Tehran
2021-05-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_81172_9ff66c3b9bbdd8cf2a12fe692c36711a.pdf |
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| author | Reza Ameri Ali Tavakoli Mohammad Hamidi |
| author_facet | Reza Ameri Ali Tavakoli Mohammad Hamidi |
| author_sort | Reza Ameri |
| collection | DOAJ |
| description | The purpose of this paper is to construct Boolean rings from multirings. In this regards, a method to construct a multigroup(multiring) on a given non-empty set, are introduced and its properties has been investigated. Also, an equivalence relation on a multiring are introduced and it is extended to an smallest strongly regular equivalence relation, such that its quotient space be a commutative Boolean ring with identity. Finally, the transitivity of this relation based on complete parts are proved. |
| format | Article |
| id | doaj-art-d6274c62ae4945c0bf8a2066a70f42db |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2021-05-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-d6274c62ae4945c0bf8a2066a70f42db2025-08-20T01:53:37ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142021-05-0132215916710.22059/jsciences.2021.295842.100748181172Boolean Rings Based On MultiringsReza Ameri0Ali Tavakoli1Mohammad Hamidi21 School of Mathematics, Statistics and Computer Sciences, University of Tehran, Tehran, Islamic Repupblic of Iran2 Department of Mathematics, Faculty of Mathematics, University of Payam-e- Noor, Tehran, Islamic Republic of Iran2 Department of Mathematics, Faculty of Mathematics, University of Payam-e- Noor, Tehran, Islamic Republic of IranThe purpose of this paper is to construct Boolean rings from multirings. In this regards, a method to construct a multigroup(multiring) on a given non-empty set, are introduced and its properties has been investigated. Also, an equivalence relation on a multiring are introduced and it is extended to an smallest strongly regular equivalence relation, such that its quotient space be a commutative Boolean ring with identity. Finally, the transitivity of this relation based on complete parts are proved.https://jsciences.ut.ac.ir/article_81172_9ff66c3b9bbdd8cf2a12fe692c36711a.pdfmultigroupmultiringfundamental relationboolean ring |
| spellingShingle | Reza Ameri Ali Tavakoli Mohammad Hamidi Boolean Rings Based On Multirings Journal of Sciences, Islamic Republic of Iran multigroup multiring fundamental relation boolean ring |
| title | Boolean Rings Based On Multirings |
| title_full | Boolean Rings Based On Multirings |
| title_fullStr | Boolean Rings Based On Multirings |
| title_full_unstemmed | Boolean Rings Based On Multirings |
| title_short | Boolean Rings Based On Multirings |
| title_sort | boolean rings based on multirings |
| topic | multigroup multiring fundamental relation boolean ring |
| url | https://jsciences.ut.ac.ir/article_81172_9ff66c3b9bbdd8cf2a12fe692c36711a.pdf |
| work_keys_str_mv | AT rezaameri booleanringsbasedonmultirings AT alitavakoli booleanringsbasedonmultirings AT mohammadhamidi booleanringsbasedonmultirings |