karmic_mishap
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 Dec 1 awarded Popular Question Nov 22 awarded Autobiographer Nov 22 revised A proof that this set is an ideal of a commutative ring corrected reasoning again... Nov 22 comment A proof that this set is an ideal of a commutative ring But they aren't. Time for a (hopefully, final) edit. Nov 22 awarded Commentator Nov 22 comment A proof that this set is an ideal of a commutative ring Just a non-invertible automorphism! Wish the textbook included this stuff. Any other good ones you would recommend? Nov 22 comment A proof that this set is an ideal of a commutative ring I like your reply, but now I need to go learn what an endomorphism is. Thanks for the new math, really! According to your reply, it must be related as the left annihilator mentioned elsewhere. I will have to look into both of them. Nov 22 comment A proof that this set is an ideal of a commutative ring Argh, didn't use the x label again when proving that -b is in R. Hopefully the technical details are all ok now, though. Nov 22 revised A proof that this set is an ideal of a commutative ring completed proof that L is an additive subgroup of R Nov 20 revised A proof that this set is an ideal of a commutative ring fixed grammar error (I'll stop now, sorry) Nov 20 revised A proof that this set is an ideal of a commutative ring added 1104 characters in body Nov 20 comment A proof that this set is an ideal of a commutative ring Thanks to both @MarianoSuárez-Alvarez and Arturo Magidin for your suggestions to approach the problem more directly. I did so at first and must have messed something up badly, because I abandoned that route and tried this tack instead. Now that I have tried it again, it seems much simpler. I will add my new approach to my question now. Nov 20 comment A proof that this set is an ideal of a commutative ring Thanks to you as well @Henning, my general intent with adding that was to only write out the unfolding explicitly. I clearly should not have done so, given the logical interpretation you have brought up! Nov 20 comment A proof that this set is an ideal of a commutative ring Thank you for your help. I was a bit worried about my calling it a kernel as well, I should be able to remember that in the future. It seems that everything I wrote about this seemingly simple map was indeed quite muddled. I appreciate the continued patience in pointing that out. Nov 20 accepted A proof that this set is an ideal of a commutative ring Nov 20 asked A proof that this set is an ideal of a commutative ring Oct 30 comment Simple properties of a direct product Thanks to both you and @AMPerrine for your helpful replies. I'll clean it up a bit soon with the feedback you've provided. Oct 30 accepted Simple properties of a direct product Oct 30 asked Simple properties of a direct product Oct 25 answered If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?