Hermite环的扩张(英文)  

Extensions of Hermite Rings

作　　者：陈焕银[1] 

机构地区：[1]杭州师范大学数学系,杭州浙江310036

出　　处：《数学进展》2015年第2期199-207,共9页Advances in Mathematics（China）

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(No.LY13A010019)

摘　　要：结合环R的理想I称为Hermite理想,如果I上的任何矩阵都可以对角化.证明了R的正则理想I为Hermite理想当且仅当对任何x∈I^2(x∈~2I),存在y∈col_2(R)(y∈row_2(R))使得xy∈I(yx∈I)是幂等元.进一步证明了任何强可分正则理想是Hermite理想;进而利用一类单位正则性刻画了Hermite正则理想。An ideal / of a ring R is Hermite provided that every matrix over I admits a diagonal reduction.We prove that a regular ideal of a ring R is Hermite if and only if for any x ∈ I^2,there exists y ∈ col_2(.R) such that xy ∈ I is an idempotent;and if and only if for any x ∈ ~2I,there exists y ∈E row_2(R) such that yx ∈ I is an idempotent.Also we show that every strongly separative regular ideal is Hermite.Based on these,we characterize Hermite regular ideals by means of a kind of unit-regularity.

关 键 词：正则理想 Hermite理想 对角化 

分 类 号：O153.3[理学—数学]