Generic matrix ring

In algebra, a generic matrix ring is a sort of a universal matrix ring.

Explicitly, it is the subalgebra of the matrix ring $M_{n}(k[(X_{l})_{ij}|1\leq l\leq m,1\leq i,j\leq n])$ generated by n-by-n formal matrices $X_{1},\dots ,X_{m}$, where $(X_{l})_{ij}$ are matrix entries and commute by definition.

References

• Artin, Michael (1999). "Noncommutative Rings" (PDF).