Yes, I think what you're saying in your third paragraph is what I was trying to say in my second paragraph. And I agree that the article could stand to be much

Yes, I think what you're saying in your third paragraph is what I was trying to say in my second paragraph. And I agree that the article could stand to be much clearer on its motivations. Re: the integers mod 7, I had a brainfart; of course the integers mod 7 are a UFD, but trivially so, as they are a field. My apologies!