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交换环上严格上三角矩阵环的自同构 被引量：2

Automorphisms of the Strictly Upper Triangular Matrix Ring over Commutative Rings
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摘要 研究了任意交换环R上的n阶严格上三角矩阵环Nn(R)的自同构 ,证明了环Nn(R)的任一自同构 The aim of this paper is to discuss the automorphisms of the strictly upper triangular matrix ring N n(R) over commutative rings. We prove that any automorphism ρ of N n(R) can be expressed as a product of standard automorphisms.
作者 谭作文 杨玉月 曹佑安
机构地区 湘潭大学数学系
出处 《湘潭大学自然科学学报》 CAS CSCD 2002年第2期1-5,共5页 Natural Science Journal of Xiangtan University
基金 国家自然科学基金资助项目 ( 198710 6 9) 湖南省教育厅资助科研项目 ( 0 1A0 0 3 0 0C0 6 5 )
关键词 交换环 严格上三角矩阵环 自同构 strictly upper triangular matrix ring automorphisms
分类号 O153.3 [理学—基础数学]
  • 相关文献

参考文献14

  • 1[1]Barker G P.Automorphisms of triangular matrices over graphs[J].Linear Algebra Appl,1992,160:63-74.
  • 2[2]Barker G P,Kezlan T P.Automorphisms of algebras of upper triangular matrices[J].Arch Math (Basel),1990,55:38-43.
  • 3[3]Barker G P.Automorphism groups of algebra of triangular matrices[J].Linear Algebra Appl,1989,121:207-215.
  • 4[4]Barker G P,Kezlan T P.The automorphism group of a matrix algebra[J].in Current Trends in Matrix Theory.Preceedings, Auburn, 1986: 33-39.
  • 5[5]Cao You'an.Automorphisms of Certain Lie algebras of upper triangular matrices over a commutative ring[J].J Algebra,1997,189: 506-513.
  • 6[6]Cao You'an.Automorphisms of Lie algebra of strictly uppertriangular matrices over certain commutative rings[J].Linear Algebra Appl,2001,329:175-187.
  • 7[7]Cao You'an, Wang Jingtong.A note of algebra automorphisms of strictly upper trian-gular matrices over commutative rings[J].Linear Algebra Appl,2000,311:187-193.
  • 8[8]Dokovc D Z.Automorphisms of the Lie algebra of upper triangular matrices over a connected commutative ring[J].J Algebra,1994,170: 101-110.
  • 9[9]Coelho S P.The automorphism group of a structural matrix algebra[J].Linear Algebra Appl,1993,195:35-58.
  • 10[10]Coelho S P.Automorphism group of certain structural matrix rings[J].Communications in Algebra,1994,22:5 567-5 586.

同被引文献18

  • 1陈陪慈.半环理论与语言和自动机[M].南昌:江西高校出版社,1993.
  • 2Barker C P.Automorphisms of triangular matrices over graphs[J]..Linear Algebra Appl, 1992,160:63-74.
  • 3Barker C P,Kezlan T P.Automorphisms of algebras of upper triangular matrices[J].Arch Math (Basel), 1990,55:38-43.
  • 4Barker G P.Automorphism groups of algebra of triangular matrices[J].Linear Algebra Appl,1989,121:207-215.
  • 5Barker G P,Kezlan T P.The automorphism group of a matrix algebra[J].In Current Trends in Matrix Theory Preceedings, Auburn,1986:33-39.
  • 6Cao You'an.Automorphisms of Certain Lie algebras of upper triangular matrices over a commutative ring[J].J Algebra,1997,189:506-513.
  • 7Cao You'an.Automorphisms of Lie algebra of strictly uppertriangular matrices over certain commutative rings[J].Linear Algebra Appl,2001,329:175-187.
  • 8Cao You'an, Chen Zhonghu, Huang Chong.Commutativity preserving linear maps and Lie automorphisms of strictly upper triangular matrix space[J],Linear Algebra Appl,2002,350:41-66.
  • 9Cao You'an, Wang Jingtong.A note of algebra automorphisms of strictly upper trian-gular matrices over commutative rings[J].Linear Algebra Appl., 2000, 311: 187-193.
  • 10Dokovc D Z.Automorphisms of the Lie algebra of upper triangular matrices over a connected commutative ring[J],J Algebra,1994,170:101-110.

引证文献2

二级引证文献1

湘潭大学自然科学学报
2002年 第2期

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