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An introduction to topological hyperrings | ||
| Caspian Journal of Mathematical Sciences | ||
| مقاله 6، دوره 9، شماره 2، آذر 2020، صفحه 210-223 اصل مقاله (126.52 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2020.19029.1527 | ||
| نویسندگان | ||
| Mehdi Nodehi1؛ Morteza Norouzi* 2؛ Omid Reza Dehghan2 | ||
| 1Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran | ||
| 2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran | ||
| تاریخ دریافت: 23 خرداد 1399، تاریخ بازنگری: 27 تیر 1399، تاریخ پذیرش: 28 تیر 1399 | ||
| چکیده | ||
| In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (closed) open subset is a complete part in a topological complete hyperring then its fundamental ring is a topological ring. Finally, we study the quotient topology induced by $\Gamma^{*}$-relation on an associated Krasner hyperring obtained by a ring and show that it is isomorphic to a quotient space of the ring by its ideals. | ||
| کلیدواژه‌ها | ||
| Topological hyperring؛ $Gamma^{*}$-relation؛ complete part؛ complete hyperring | ||
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آمار تعداد مشاهده مقاله: 471 تعداد دریافت فایل اصل مقاله: 604 |
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