Should we answer questions like What is the difference between field and group in algebra ? I mean, how can someone serious about learning ask this here instead of looking it up in a textbook or in wikipedia?
I think this type of question is too broad. The asker should specify what part of the definitions he didn't understand. And if it was not about definitions, he should explain what was the purpose of the question.
I don't see why such a question shouldn't be allowed.
In fact I think it's a completely reasonable question, and one can imagine that the person asking is looking not just for a literal description of the difference (which they can presumably see for themselves by looking at the axioms of each structure and noting that they are different), but some cultural explanation of the differences, e.g. an explanation of what the two concepts are trying to model.
I believe questions of this kind should be answered with as much good faith as possible.
I am not alone as there has been at least two answers when I first read this tread.
It seems there are two different kind of value that an expert can bring to a Q&A user:
precise, very factual, hard to find knowledge, digested and technically sound explanations, essentially closing a question, allowing the asker to use the answer directly for an application.
broad, synthetic, first outline of context and what is at stake, giving a perspective to someone who risks to loose himself in technical details or is just too new to have a good grasp of methodology and classical references.
To try to be coherent with my opinion, I have added a third answer to the question that motivated this thread. And I am interested by your opinion.
If S.E. is all about giving answerers a good environment, the illusion to be able to transmit their hard-earned intuition or personal broad picture could be part of that environment and motivation. And the occasion of confronting his or her vision with those of other experts and practitioners is fun. I believe this is already what happened.