Suppose R is a principal ideal ring, R^＊ is a multiplicative group which is composed of all reversible elements in R, and Mn（R）, GL（n,R）, SL（n,R） are denoted by,Mn（R）={A=（aij）n×n｜aij∈R,i,j=1,2…,n},G...Suppose R is a principal ideal ring, R^＊ is a multiplicative group which is composed of all reversible elements in R, and Mn（R）, GL（n,R）, SL（n,R） are denoted by,Mn（R）={A=（aij）n×n｜aij∈R,i,j=1,2…,n},GL（n,R）={g｜g∈Mn（R）,det g∈R^＊},SL（n,R）={g∈GL（n,R）｜det g=1},SL（n,R）≤G≤GL（n,R）（n≥3）,respectively,then basing on these facts, this paper mainly focus on discussing all extended groups of Gr={（O D^A B）∈G｜A∈GL（r,R）,（1≤r〈n）}in G when R is a principal ideal ring.展开更多
Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2 A 2l?1, 2 D l , 2 E 6, 3 D 4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that su...Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2 A 2l?1, 2 D l , 2 E 6, 3 D 4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that subgroups exist between the Steinberg groups over the rings D and K under some restrictions on the ring D.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10771093）
文摘Suppose R is a principal ideal ring, R^＊ is a multiplicative group which is composed of all reversible elements in R, and Mn（R）, GL（n,R）, SL（n,R） are denoted by,Mn（R）={A=（aij）n×n｜aij∈R,i,j=1,2…,n},GL（n,R）={g｜g∈Mn（R）,det g∈R^＊},SL（n,R）={g∈GL（n,R）｜det g=1},SL（n,R）≤G≤GL（n,R）（n≥3）,respectively,then basing on these facts, this paper mainly focus on discussing all extended groups of Gr={（O D^A B）∈G｜A∈GL（r,R）,（1≤r〈n）}in G when R is a principal ideal ring.
文摘Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2 A 2l?1, 2 D l , 2 E 6, 3 D 4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that subgroups exist between the Steinberg groups over the rings D and K under some restrictions on the ring D.
