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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2011-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdf |
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| Summary: | 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. |
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| ISSN: | 1016-1104 2345-6914 |