Ring Reguler Stable Diperumum

YULIZA, Evi, Prof.Dr. Sri Wahyuni, MS

2004 | Tesis | S2 Matematika

Suatu ring R merupakan ring stable diperumum jika aR + bR = R maka ada y Î R sehingga a + by Î K(R). Disini K(R) adalah himpunan {xÎRsimbol($s, t Î R) sxt = 1}. Suatu ring R dikatakan ring reguler apabila untuk setiap x di R ada y di R sehingga x = xyx. Dalam tulisan ini akan diselidiki syarat perlu dan cukup ring reguler R merupakan ring stable diperumum. Elemen x di R disebut invers refleksif dari a di R apabila a = axa dan x = xax. Dibahas pula sifat – sifat invers refleksif atas ring reguler stable diperumum. Jika a, b ÎR maka a disebut similar semu terhadap b di R apabila ada x, y, z Î R sehingga xay = b, zbx = a, xyx = x dan xzx = x. Selain itu dibahas pula sifat – sifat similar semu atas ring reguler yang memenuhi ring stable diperumum.

A ring R is generalized stable ring provided that aR + bR = R implies there exists y ÃŽ R such that a + by ÃŽ K(R) where K(R) = {x ÃŽ R simbol($s, t ÃŽ R ) sxt = 1}. A ring R is said to be regular provide that for any x ÃŽ R, there exists y ÃŽR such that x = xyx. In this paper, we investigate necessary and sufficient conditions that a regular ring R is generalized stable ring. We say that x ÃŽR is a reflexive inverse of aÃŽR if a = axa and x = xax. Also, we disscused reflexive inverse properties over generalized stable regular rings. If a, b ÃŽR then we say a is pseudo-similar to b in R provided that there exists x, y, z ÃŽ R such that xay = b, zbx = a, xyx = x and xzx = x . Beside that, we disscused pseudo-similar properties over regular ring satisfying generalized stable ring.

Kata Kunci : ring reguler, ring stable diperumum, invers refleksif, similar semu, regular ring, generalized stable ring, reflexive inverse, pseudosimilar