Li Fuan
Let A and R be commutative rings,and m and n be integers≥3.It is proved that,if Λ:Stm(A)→Stn(R) is an isomorphism,then m=n.When n≥4,we have: (1) Every isomorphism Λ:Stn(A)→Stn(R) induces an isomorphism λ:En(A)→En(R),and Λ is uniquely determined by if St λ; (2) If Stn(A)≡Stn(R) then K2.n(A)≡K2.n(R); (3) Every isomorphism En(A)→En(R) can be lifted to an isomorphismStn(A)→Stn(R); (4)Stn(A)≡Stn(R) if and only if A≡R.For the case n=3,if St3(A) and St3(R) are respectively central extensions of E3(A) and E3(R),then the above (1) and (2) hold.