Modular Automorphisms of Triangular Matrices over Commutative Rings Preserving Involutory

Modular Automorphisms of Triangular Matrices over Commutative Rings Preserving Involutory and

Tripotent

唐孝敏;曹重光

【期刊名称】《东北数学：英文版》 【年(卷),期】2003(019)002

【摘要】Suppose R is a commutative ring with 1, and 2 is a unit of R. LetTn(R) be the n× n upper triangular matrix modular over R, and let Li(R) (i=2 or 3) be the set of all R-module automorphisms on Tn(R) that preserve involutory or tripotent. The main result in this paper is that f∈Li(R) if and only if there exists an invertible matrix U∈Tn(R) and orthogonal idempotent elements el, e2, e3 and e4 in R with 4↑∑i=1 = 1 such that f(X) =U ((e1 -e2)x + (e3 -e4)Xδ) U-1' VX∈Tn(R),where Xδ = (Xn+1-j n+1-i).

【总页数】6页(P.149-154)

【关键词】交换环;三角矩阵;保对合矩阵;保立方幂等矩阵;模自同构;局部化;线性保存问题

【作者】唐孝敏;曹重光 【

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DepartmentofMathematics,HarbinInstituteofTechnology,Harbin,150001；DepartmentofMathematics,HeilongjiangUniversity,Harbin,150080;DepartmentofMathematics,HeilongjiangUniversity,Harbin,150080