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 17h answered Simple generator modules 2d comment if the sum of two units is a unit, then there is an unique maximal ideal @RobbeMotmans What good is insisting on what your book says when you have just been shown that this is false in rings other than $\{0\}$? The question with "units" replaced with "nonunits" appears many times already here on math.SE. 2d comment Why do lines in the poincare model meet the infinite edge at right angles? So you want an explanation that assumes the hyperbolic sheet model, and you want to see how that makes the right angles in the Poincare model? Apr23 revised $X$ is A-space iff the frontier of any closed set in $X$ is compact. edited title Apr23 comment Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$? This question gets asked from time to time, but it looks like the duplicates are hard to track. This one also adds the question about finite generation, so maybe others will become duplicates of this. Apr23 answered What are all the integral domains that are not division rings? Apr22 comment Show that if $r$ is nilpotent in a ring with identity, then $1-r$ is a unit in $R$ This is the third question you've asked recently closed because it duplicates many previous questions. Please take advantage of the search feature before you ask a question. Apr22 answered Why is it called the category of representations? Apr22 answered Uniqueness of prime ideals of $\mathbb F_p[x]/(x^2)$ Apr22 comment Nilpotent elements in group algebra Interesting! I have not seen this reference before. Apr21 comment Nilpotent elements in group algebra Are we sure this question has a positive answer? Where did it come from? Apr21 revised Problems with understanding the proof of noetherian ring added 316 characters in body Apr21 comment Problems with understanding the proof of noetherian ring @user136266 Incidentally, what user73985 says is just fine. Submodules of submodules are submodules. Apr21 comment Problems with understanding the proof of noetherian ring @user136266 Certainly not. I think I may see the source of your confusion, and I expanded my answer a bit to explain. Let me know if it's helpful or not. Apr21 revised Problems with understanding the proof of noetherian ring added 939 characters in body Apr21 answered Problems with understanding the proof of noetherian ring Apr21 revised Some theorems in euclidean geometry have incomplete proofs Removing tags that don't fit Apr21 comment Is the zero ideal $\{0_{M_2(\mathbb{R})}\}$ maximal in $M_{2}(\mathbb{R})$? @Jellyfish : $M_2(\Bbb R)$ is not a division ring. Apr20 comment Bourbaki Algebra Chapter IV - Exercise 9(b) By forcing readers to go find this book, you are screening out most of the audience capable of helping you. Even if someone has that book and wants to help you, maybe they can't be bothered to look up the whole problem for you. You have it right there, just write it down... Apr20 revised Characteristic of a Finite Integral Domain added 513 characters in body