Ring hasil bagi untuk Ring Komutatif dan Ring Nonkomutatif

RATNASARI, Lucia, Prof.Dr. Sri Wahyuni, MS

2005 | Tesis | S2 Matematika

Jika R ring komutatif dan S himpunan bagian multiplikatif dari R , maka dengan menggunakan prosedur lokalisasi R pada S dihasilkan suatu Ring Hasil Bagi S R dengan elemen-elemen berbentuk s r dengan r ÃŽ R dan sÃŽS . Jika R ring nonkomutatif dan S himpunan bagian multiplikatif dari R maka diperlukan syarat tambahan pada S untuk mengetahui eksistensi dari Ring Hasil Bagi Kanan (Kiri). Jika S adalah permutable kanan (kiri) dan reversible kanan (kiri) maka S disebut himpunan denominator kanan (kiri). Ring R mempunyai ring hasil bagi kanan (kiri) terhadap S jika dan hanya jika S adalah himpunan denominator kanan (kiri).

Let R be a commutative ring and S be a multiplicative subset of R . Then by using localization procedure on R with respect to S we could construct Ring of Quotients S R with every element in S R can be written as s r where r ÃŽ R and sÃŽS . For a noncommutative ring R and a multiplicative subset S in R , the right (left) ring of quotient s does not exist for every S . A necessary condition of existence right (left) ring of quotients is S right (left) permutable and right (left) reversible. A multiplicative subset S is called a right (left) denominator if it is right (left) permutable and right (left) reversible. The ring R has a right (left) ring of quotients with respect to S if and only if S is a right (left) denominator set.

Kata Kunci : Ring Hasil Bagi, Ring Komutatif dan Nonkomutatif, ring of quotients, right (left) ring of quotients, localization, right (left) permutable, right (left) reversible, right (left) denominator