Talk:Lattice (module)
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Torsion-free
[edit]A parenthetical defininition of "torsion-free" was "no non-zero element of M is annihilated by a non-zero element of R", which is the usage of Reiner (2003) page 44, the source cited. Another editor wants to replace non-zero element of R by regular element of R, which is not consistent with the source, although it is the same in this context as the ring R is already assumed to be an integral domain. This seems wrong. Deltahedron (talk) 07:44, 21 March 2014 (UTC)
Just think about how you would generalize this to the case R is not an integral domain. Let $x\in L$ and $a,b \in R$ such that $a, b \neq 0$ but $ab=0$. Then $0\neq bx \in L$, but $0 = a(bx)= (ab)x$. Unless you find a fault with my argument, I feel I have to revert again to my last edit, because it makes more sense to keep Wikipedia internally consistent, than consistent with the sources it cites. And in this case, we want to give the same definition here of "torsion-free" that is on the page for "torsion-free" Wisapi (talk) 18:07, 1 July 2014 (UTC)
- Here on Wikipedia we go by what can be verified by reference to independent reliable sources. My view of your argument is not the point. Deltahedron (talk) 19:59, 1 July 2014 (UTC)