Let $k$ be a countable field and $C$ be the ring of $k$ linear transformations of a countably infinite dimensional $k$ vector space. Let $S$ be the socle of $C$, which is the unique nontrivial ideal. Let $B$ be the subring of $C$ generated by $S$ and the identity of $C$. The required ring is $B\otimes_kB$
Keywords endomorphism ring subring tensor product
Name | Measure | |
---|---|---|
global dimension | left: 2 | right: 1 |
weak global dimension | 0 |
Name | Description |
---|---|
Jacobson radical | $\{0\}$ |
Left singular ideal | $\{0\}$ |
Right singular ideal | $\{0\}$ |