A Strong Regular Relation on ?-Semihyperrings
The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semih...
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University of Tehran
2011-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdf |
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| author | B Davaz |
| author_facet | B Davaz |
| author_sort | B Davaz |
| collection | DOAJ |
| description | The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyperrings and a generalization of ?-semirings. In this paper, we introduce an equivalence relation ?* on a ?-semihyperrings R and we show that it is strongly regular. Furthermore, R/?*, the set of all equivalence classes of this relation is a ?/?*-semiring. The relation ?* is called the fundamental relation and the ?-semiring R/?* is called the fundamental semiring. Fundamental relations are the main tools in the study of ?-semihyperrings. We present some results about fundamental relations and fundamental semirings. Finally, we show that there is a covariant functor between the category of ?-semihyperrings and the category of semirings. |
| format | Article |
| id | doaj-art-1ddb957bca71441c964d6fe644b14535 |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2011-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-1ddb957bca71441c964d6fe644b145352025-08-20T03:53:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142011-09-0122325726623588A Strong Regular Relation on ?-SemihyperringsB Davaz0Yazd UniversityThe concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyperrings and a generalization of ?-semirings. In this paper, we introduce an equivalence relation ?* on a ?-semihyperrings R and we show that it is strongly regular. Furthermore, R/?*, the set of all equivalence classes of this relation is a ?/?*-semiring. The relation ?* is called the fundamental relation and the ?-semiring R/?* is called the fundamental semiring. Fundamental relations are the main tools in the study of ?-semihyperrings. We present some results about fundamental relations and fundamental semirings. Finally, we show that there is a covariant functor between the category of ?-semihyperrings and the category of semirings.https://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdffundamental semiring?-semihyperring?-hyperringstrongly regular relation |
| spellingShingle | B Davaz A Strong Regular Relation on ?-Semihyperrings Journal of Sciences, Islamic Republic of Iran fundamental semiring ?-semihyperring ?-hyperring strongly regular relation |
| title | A Strong Regular Relation on ?-Semihyperrings |
| title_full | A Strong Regular Relation on ?-Semihyperrings |
| title_fullStr | A Strong Regular Relation on ?-Semihyperrings |
| title_full_unstemmed | A Strong Regular Relation on ?-Semihyperrings |
| title_short | A Strong Regular Relation on ?-Semihyperrings |
| title_sort | strong regular relation on semihyperrings |
| topic | fundamental semiring ?-semihyperring ?-hyperring strongly regular relation |
| url | https://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdf |
| work_keys_str_mv | AT bdavaz astrongregularrelationonsemihyperrings AT bdavaz strongregularrelationonsemihyperrings |