IDEAL HAMPIR PRIMAL PADA RING KOMUTATIF

AZZA SUNDUS ANTARTIKA, Prof. Dr. Sri Wahyuni, M.S. ; Sutopo, S.Si., M.Si.

2015 | Skripsi | S1 MATEMATIKA

Dalam tugas akhir ini dibahas tentang ideal hampir prima, ideal hampir primal, dan ideal hampir primary dari ring komutatif dengan elemen satuan. Suatu ideal I dikatakan hampir prima dari R jika untuk setiap a,r elemen R berlaku bahwa jika ra elemen I-I^ maka a elemen I atau r elemen I. Ideal hampir prima merupakan perumuman dari ideal prima. Setiap ideal prima merupakan ideal hampir prima, tapi suatu ideal hampir prima belum tentu merupakan ideal prima. Suatu elemen a di R disebut elemen hampir prima terhadap ideal I jika untuk setiap r elemen R berlaku bahwa jika ra elemen I-I^ maka r elemen I. Akibatnya, suatu elemen a elemen R disebut elemen bukan prima terhadap ideal I jika terdapat r elemen R-I, sehingga ra elemen I-I^. Selanjutnya, himpunan dari elemen di R yang bukan elemen hampir prima terhadap ideal I dinotasikan dengan A(I). Ideal I dikatakan ideal hampir primal dari ring R jika himpunan A(I) gabung himpunan I^ merupakan suatu ideal dari R.

In this final project, we discuss about almost prime ideal, almost primal ideal, and almost primary ideal in commutative ring with identity. An ideal $I$ is called almost prime ideal of R if for a,r element R, ar element I-I^ implies a element I or r\in I. Almost prime ideal is a generalization of prime ideal. Every prime ideal is almost prime ideal, but an almost prime ideal not always be prime ideal. An element a element R is called almost prime to I provided that ra element I-I^ (for any r element R) implies that r element I. So, An element a element R is called not almost prime to I provided that ra element I-I^ for some r element R-I. The set of all elements of R that are not almost prime to I is denote by A(I). Ideal I is called almost primal ideal of R if the set A(I) union I^ forms an ideal of R.

Kata Kunci : Ideal hampir prima, Ideal hampir primary, Ideal hampir primal