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The point of MO is that highly technical questions may be only answerable by relatively few people and having these questions online allows for a better chance that an expert can answer them. An interesting question at the beginning graduate level that is not suitable for MO and perhaps too hard for most MSE users is the kind of question you can probably find someone in your math department (assuming you are at a university) to answer.
@ToddTrimble Point taken that it's the community's task to make these decisions and I guess my criticism should be directed to them also. But one thing that bothers me is a number of users who pose bad question after bad question, some get closed, others just ignored but they keep polluting the front page. If something is to be done about that, it's the moderators who have to do it. Anyway, this comment is off-topic to the present discussion and getting long already.
I just added a comment to the question sketching an answer. This is perhaps a tricky exercise in algebra, which requires knowing about real fields, but is not a research question.
