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All Journal Media Statistika BAREKENG: Jurnal Ilmu Matematika dan Terapan Variance : Journal of Statistics and Its Applications Tensor: Pure and Applied Mathematics Journal Mathematics and Applications (MAp) Journal Eksponensial
H. W. M. Patty
Jurusan Matematika FMIPA Universitas Pattimura Ambon
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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Journal : Mathematics and Applications (MAp) Journal

 1 
S-RING KELAS INTERVAL NATURAL Patty, Dyana; W. M. Patty, Henry
MAp (Mathematics and Applications) Journal Vol 2, No 1 (2020)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (920.947 KB) | DOI: 10.15548/map.v2i1.1633

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.AbstractThis 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.
Co-Authors Abdul H. Mahmud Abraham Z. Wattimena Adya Afriananda Chevano Bill Pattipeilohy Elvinus R. Persulessy Fandy Sanudin Feros Maitimu Ferry Kondo Lembang Ikbal Muhammad Lidia Salaka Marlon S. Noya van Delsen Marlon Stivo Noya Van Delsen Melky M. Romsery Mozart W. Talakua Muhammad Yahya Matdoan Natalia Kelbulan Patty, Dyana RAHAKBAUW, DORTEUS LODEWYIK RUMLAWANG, FRANCIS YUNITO Salmon N. Aulele Salmon N. Aulele Salmon Noce Aulele Trisnawaty Trisnawaty Y. A. Lesnussa Yohana Y. Bakarbessy