Does there exist a non-trivial ring $R$ such that $R\cong R[X]$? ($R[X]$ denotes the polynomial ring over $R$). If not, how does one prove it? Else, an example of such a ring and the respective isomorphism is appreciated. Thank you.
Asked
Active
Viewed 61 times
1
-
2Hint: You can take $R=\mathbb{Z}[x_1,x_2,\dots ]$. – Pax Oct 16 '21 at 18:54
-
Thank you pax :). That works. didn't cross my mind. – RichardAshcroft Oct 16 '21 at 18:59
-
1I’m sure there is a duplicate answering with the infinite polynomial ring but I haven’t found it yet. I’m linking for the time being to another interesting distinct example. – rschwieb Oct 16 '21 at 23:08