>>12076681I don't know, could you tell me at all about Kenneth Ireland? No, but they wrote a pretty well respected book on number theory.
But fine, I have another example. Literally next algebra book I pulled out, Basic Algebra 1. By Nathan Jacobson. Nathan Jacobson is, in the context of mathematicians, one of the better known ones, known for his work on the structure theory of ring. And as far as references go, I've seen this one pop up again and again. (what, want to check Lang next?) Here we have the exact same thing on page 117. [and there isn't a preview for that page but if you don't have the book and doubt me just go to this sketchy website here
https://b-ok.org/book/2378520/c9bf02 and download it]
And for the hell of it, here is Lang, who is a quite well known textbook writer:
https://math24.files.wordpress.com/2013/02/algebra-serge-lang.pdf#page=123 and once again, we see exactly as I've said.
Oh, and that book by Ireland and Rosen I also checked for the hell of it:
https://www.google.com/books/edition/A_Classical_Introduction_to_Modern_Numbe/HlHuBwAAQBAJ?hl=en&gbpv=1&pg=PA13&printsec=frontcover, you can see in the middle here the notation also used.
At the very least shift the goalposts of your argument-you've been clearly shown wrong.
