(All rings here are always assumed to be unital and associative). Setup Let $R$ be a ring, and $A$ and $B$ be $R$-algebras, with $A$ a commutative subalgebra of $B$ satisfying: If $u$ is a unit ...
The notion of dimension I prefer most is right global dimension, but the question can also be asked for other notions (e.g. weak dimension, injective dimension, Krull dimension). Letting $d$ be ...
If n is given and A is a subalgebra of M_n(C), the algebra of n-by-n matrices with entries in the field of complex numbers, then what are the possible values of dimension of A as a vector space over ...