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A Strong Regular Relation on ?-Semihyperrings | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 5، دوره 22، شماره 3، آذر 2011، صفحه 257-266 اصل مقاله (283.45 K) | ||
| نویسنده | ||
| B Davaz | ||
| Yazd University | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fundamental semiring؛ ?-semihyperring؛ ?-hyperring؛ Strongly regular relation | ||
| عنوان مقاله [English] | ||
| A Strong Regular Relation on ?-Semihyperrings | ||
| نویسندگان [English] | ||
| B Davaz | ||
| چکیده [English] | ||
| 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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