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I asked this question here. I know it is an "immediate consequence of the theorem", and sometimes we only understand the theorem and don't know how to apply the theorem in an example. So, I wanted to learn how to apply the Fundamental Theorem of Homomorphisms for rings in that example, but I keep getting downvotes. I always try to show what I did as attempts for whatever questions I asked. But, I couldn't do that for that particular post, since I really don't know how to proceed. Is that why I am losing my reputation points? Besides that what exactly is wrong with my question?

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    $\begingroup$ I would guess that one of the most apparent problems is that your question is not self-contained. It will also help to state that you're learning this stuff, so that it's at least clear where you stand. $\endgroup$ – Lord_Farin Mar 9 '15 at 22:03
  • $\begingroup$ I thought it is really obvious that I am completely new to this stuff. $\endgroup$ – Jellyfish Mar 9 '15 at 22:08
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    $\begingroup$ Nothing is obvious on the internet. $\endgroup$ – Gerry Myerson Mar 9 '15 at 22:53
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    $\begingroup$ I suggest seeing an individual tutor, in person. Perhaps your college ha a tutoring center, either within the mathematics department or elsewhere. If you are doing this on your own, you may be out of luck: I'm not sure about years ago, when this site began, but I don't, these days, compose lengthy tutorials on MSE about material that is covered in the (presumed) textbook. $\endgroup$ – Will Jagy Mar 9 '15 at 22:57
  • $\begingroup$ Thanks for you suggestion. Before I ask anything here, I make sure I searched through the internet to find anything useful on that matter, and then I ask here. Also, another reason for me to ask a question here because I thought maybe there are people like me here who could help me understand the problem in a not so complicated way if that makes any sense to you. $\endgroup$ – Jellyfish Mar 9 '15 at 23:26
  • $\begingroup$ In case this gets noticed: I was not suggesting individual tutoring as a reference on how to post a better question on MSE. I suggest that because the signs are that nothing short of some help from a knowledgeable human being in the same room will help, not MSE, also not Skype or whatever video chat service people use now. $\endgroup$ – Will Jagy Mar 10 '15 at 19:03
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At the very least, when you ask for help applying a specific theorem you should include the theorem you want help on in the question. It is okay to copy it verbatim from a textbook (or wherever you have learned that such-and-such is a theorem), but seeing the theorem itself in the question is necessary before anyone can start answering it.

Just giving the name of the theorem is not enough -- different books use the same name for theorems that are slightly different (sometimes equivalent, sometimes not), or use different symbols and letters for the assumptions, and so forth.

One cannot start helping you without knowing exactly what the assumptions and conclusions of the theorem you're looking at is, and what those different assumptions are called in the text you're reading. Otherwise one risks ending up in confusion because what I call $A$ is the thing your book calls $B$ and vice versa.


Concretely, your question seems to fail to explain what $f$ is. It is worded as if $f$ is some map the reader is supposed to know already what is, but since you're not including that information in your question, it is anyone's guess what $im(f)$ is.

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