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Let R_1,R_2$R_1,R_2$ be (left and right) ore domains. Does $ Mat_n(R_1)\cong Mat_m(R_2)$ impliesimplie m=n and $q.f.(R_1)\cong q.f.(R_2)$?

An counter example, a proof or a reference is welcomed.

Thanks

Let R_1,R_2 be (left and right) ore domains. Does $ Mat_n(R_1)\cong Mat_m(R_2)$ implies m=n and $q.f.(R_1)\cong q.f.(R_2)$?

An counter example, a proof or a reference is welcomed.

Thanks

Let $R_1,R_2$ be (left and right) ore domains. Does $ Mat_n(R_1)\cong Mat_m(R_2)$ implie m=n and $q.f.(R_1)\cong q.f.(R_2)$?

An counter example, a proof or a reference is welcomed.

Thanks

Source Link
rrr
rrr
  • 53
  • 3

Isomorphism of matrix ring over ore domain

Let R_1,R_2 be (left and right) ore domains. Does $ Mat_n(R_1)\cong Mat_m(R_2)$ implies m=n and $q.f.(R_1)\cong q.f.(R_2)$?

An counter example, a proof or a reference is welcomed.

Thanks