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 May15 revised Application of Galois theory Taking comments into account May15 awarded Commentator May15 comment Application of Galois theory @Qiaochu : right, it was developed around that particular problem but is not restricted to it. I will change my wording. May15 revised Application of Galois theory Added examples May15 answered Application of Galois theory May12 awarded Vox Populi May12 awarded Suffrage May12 awarded Critic Apr27 revised Set of Ideals of a Polynomial Ring changed title to avoid a confusion with another question Apr27 revised Prime Ideal of a Polynomial Ring changed title and beautified the set of rationals Apr27 suggested approved edit on Prime Ideal of a Polynomial Ring Apr27 suggested approved edit on Set of Ideals of a Polynomial Ring Apr26 answered Books and Papers that have treatment of properties like Idempotence and related operations Apr25 awarded Quorum Apr25 revised what is the difference between field and group in algebra Another edit, illustrating that it is sometimes more risky to stay in generalities than to use only definitions and theorems. Apr25 comment what is the difference between field and group in algebra @Mariano: you are right the confusion stems from the meaning of "parent" in french which is more inclusive than in modern english. I will edit my text again, thanks for your remark. But I maintain that there is a stronger and genetic link between groups and rings than between (to take your own example), topological spaces and groups, even if in my opinion, the latter link is quite close too. Apr25 comment what is the difference between field and group in algebra @Mariano: About rings, the problem between us is perhaps the meaning of "parent" here. I see at least two reasons to consider them close parents : one is the embedded group in a ring and another one is the fundamental way to see a finite group for instance, as a $\Z$-module or a $F_q$-module. It is the basis of modern proofs of many important results of group theory. Apr25 revised what is the difference between field and group in algebra Try to respect the Vulgate on the HotGC Apr25 comment what is the difference between field and group in algebra My formulation -- I will try to edit it, may give a false impression. Groups actually arose first under this name both in the study of equations designed and used by Galois as "Groups of substitutions" operating on symbols and by Cauchy as well, at the same time, operating also on points of geometrical figures designed by letters. Apr25 answered what is the difference between field and group in algebra