Timeline for Non-zero homomorphism from a module to its ground ring

4 events

when toggle format	what		by	license	comment
Dec 15, 2018 at 4:28	comment	added	Andreas Blass		In my previous comment, "greatest common divisor" should have been "least common multiple". (Sometimes it would be nice to be able to edit comments.)
Dec 13, 2018 at 16:02	comment	added	David Handelman		@AndreasBlass ... and a finitely generated torsion-free module over a Dedekind domain (${\bf Z}[\zeta]$) is projective, so yes, there exist lots of homomorphisms to $R$.
Dec 13, 2018 at 15:21	comment	added	Andreas Blass		It seems to me that the $\alpha=\beta$ case is the general case. If $\alpha$ is a primitive $k$-th root of unity and $\beta$ is a primitive $l$-th root of unity, let $d$ be the greatest common divisor of $k$ and $l$, let $\zeta$ be a primitive $d$-th root of unity, and notice that $\mathbb Z[\alpha,\beta]=\mathbb Z[\zeta]$.
Dec 13, 2018 at 14:57	history	asked	Alireza Abdollahi	CC BY-SA 4.0