Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved ...Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,
