摘要
本文的主要结果如下 :( 1)环R关于其乘法封闭子集S满足左Ore条件当且仅当R[σ1 ,σ2 ,… ,σt]关于其相应乘法封闭子集S[σ1 ,σ2 ,… ,σt]满足左Ore条件 .( 2 )若R关于其乘法封闭子集S满足左Ore条件 ,S- 1 R是R关于S的左分式环 ,其自然同态为 φ∶R →S- 1 R ,则存在环同态 φ ∶R[σ1 ,σ2 ,… ,σt] →S[σ1 ,σ2 ,… ,σt] - 1 R[σ1 ,σ2 ,… ,σt]使得(S- 1 R) [ φ(σ1 ) , φ(σ2 ) ,… , φ(σt) ] S[σ1 ,σ2 ,… ,σt] - 1 R[σ1 ,σ2 ,… ,σt] .
The main results of the paper are that a r ing Rsatisfies the left Ore conditions with respect to its multiplicatively cl osed subset S if and only if so does R[σ 1,σ 2,…,σ t] with resp ect to its relevant multiplicatively closed subset S[σ 1,σ 2,…,σ t] and that if R satisfies the left Ore conditions with respect to S and S -1 R is a left ring of fractions of R with respect to S with t he natural ring homomorphism φ∶R→S -1 R,then there is a ring homomorp hism ∶R[σ 1,σ 1,…,σ t]→S[σ 1,σ 2,…,σ t] -1 R [σ 1,σ 2,…,σ t] such that(S -1 R)[(σ 1),( σ 2),…,(σ t)]S[σ 1,σ 2,…,σ t] -1 R[σ 1,σ 2,… ,σ t].
出处
《应用数学》
CSCD
北大核心
2003年第4期117-121,共5页
Mathematica Applicata
基金
ThisresearchissupportedbyNationalScienceFoundationGrandNo .6 9972 0 36
