Uniqueness is hopeless; let $k$ be any reduced ring and $R=k[x]$. Then $k\subset R$ and $R\subset R$ have the same group of units.
Existence is also hopeless in general: Let $S=Z/5Z$, and let $H$ be the subgroup conisting of 1 and 4.
|
2 | added 8 characters in body | ||
|
|
||||
|
|
1 |
|
||
|
Uniqueness is hopeless; let $k$ be any ring and $R=k[x]$. Then $k\subset R$ and $R\subset R$ have the same group of units. Existence is also hopeless in general: Let $S=Z/5Z$, and let $H$ be the subgroup conisting of 1 and 4. |
||||
