Ring Reguler yang Memenuhi Sifat Stable Range One

Evi Yuliza

Abstract


Suatu ring R dikatakan ring reguler apabila untuk setiap x di R terdapat y di R sehingga x = xyx. Suatu ring R dikatakan memenuhi sifat stable range one apabila kondisi berikut dipenuhi yaitu: jika aR + bR = R maka terdapat suatu y 2 R sehingga a + by 2 U(R) dengan U(R) adalah himpunan semua unit dalam R. Suatu ring R dikatakan unit reguler apabila untuk setiap x 2 R terdapat suatu unit u 2 R sehingga xux = x. Penelitian ini akan menunjukkan bahwa ring reguler yang memenuhi sifat stable range one adalah unit reguler.


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References


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DOI: https://doi.org/10.56064/jps.v13i3.131

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