S-RING KELAS INTERVAL NATURAL

Dyana Patty, Henry W. M. Patty

Abstract


Artikel ini memperkenalkan kelas baru interval yang disebut kelas interval natural. Perlu dijelaskan bahwa kelas dalam artikel ini bukanlah kelas yang terbentuk karena relasi ekuivalensi dan kata natural tidak merujuk pada himpunan bilangan asli. Diberikan [x,y] adalah interval tutup dari Z atau Q atau R atau Z_n dengan n<∞. Interval tutup [x,y] disebut interval naik jika x<y, interval tutup [x,y] disebut interval turun jika x>y dan interval tutup [x,y] disebut interval merosot jika x=y. Hal yang sama juga berlaku untuk interval buka, interval buka tutup dan interval tutup buka. Koleksi interval naik, interval turun dan interval merosot selanjutnya disebut kelas interval natural. Dalam artikel ini akan dibahas struktur ring yang dibangun oleh kelas interval natural beserta sifat-sifatnya. Lebih lanjut akan diberikan syarat cukup agar suatu ring kelas interval natural merupakan -ring kelas interval natural.

Abstract

This paper introduces a new class of interval called the natural class of interval. Throughout this paper, the word class does not refer to class that formed by equivalence relation, and the word natural does not refer to the set of natural numbers. Let [x,y] be a closed interval from Z or Q or R or Z_n where  n<∞. If x<y then define [x,y] as increasing closed interval. If x>y then [x,y] is decreasing closed intervals and if x=y then [x,y] define  as degenerate closed interval. The same thing applied to an open interval, half open  and half closed interval. Let the collection of all increasing intervals, decreasing intervals and degenerate intervals defined as natural class of interval. This paper discuss about structure of ring generated by natural class of interval and their properties. Furthermore  we also give  several conditions of ring of natural class of interval to be -ring of natural class of interval.


Keywords


Interval merosot, interval naik, interval turun, ring kelas interval natural, -ring kelas interval natural

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DOI: https://doi.org/10.15548/map.v2i1.1633
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References


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