广义矩阵环的Hilbert性和稳定性

Hilbert Property and Stability of Generalized Matrix Rings

用经典环论方法证明了对于广义矩阵环Λ=〔RMNS〕,Λ是Hilbert环(或满足S-稳定秩环)当且仅当R与S都是Hilbert环(或满足S-稳定秩环).

For a generalized matrix ring Λ=〔RMNS〕, we showed that Λ is a Hilbert ring（resp.a ring satisfying S-stable range） if and only if R and S are Hilbert rings by means of classical method in ring theory.