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Journal of Sciences Islamic Republic of Iran، جلد ۲۲، شماره ۳، صفحات ۲۵۷-۲۶۶
عنوان فارسی A Strong Regular Relation on ?-Semihyperrings
چکیده فارسی مقاله 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.
کلیدواژه‌های فارسی مقاله
عنوان انگلیسی A Strong Regular Relation on ?-Semihyperrings
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Fundamental semiring, ?-semihyperring, ?-hyperring, Strongly regular relation
نویسندگان مقاله b دواز |
yazd university
سازمان اصلی تایید شده: دانشگاه یزد (Yazd university)

نشانی اینترنتی http://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdf
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