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I have read an article on the BBC website about Japan's general election and it includes the following sentence :

Japan PM has been facing open rebellion from opponents within his party.... .

shouldn't be like this :

Japan PM has been facing an open rebellion from opponents within his party.... .

thanks in advance
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Both versions (with or without "an") are OK.

However, the start of the sentence is not right (except in a telegraphic style of English that might be used, say, for a headline -- but the rest of the sentence doesn't look like a headline). It should be "Japan's PM...", or, better IMO, "Japan's Prime Minister...". Possibly there was a glitch in your copying.