Generalized Biderivation Of Triangular Algebra
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摘要: 设U=Tri(A,M,B)是三角代数，双线性映射#是U上的广义双导子。本文利用算子论的方法讨论了三角代数上的广义双导子的相关性质，并在此基础上给出了三角代数上广义双导子的一种新的刻画。
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关键词:
- 广义双导子
Abstract: Let U=Tri(A,M,B) be a triangular algebra. A bilinear map # is called a generalized biderivation if it is a generalized derivation with repect to both arguments. In this paper, by using of operator theory methods, we provide the relational characterizations of every generalized biderivation on triangular algebra U. On this basis, We obtained a new form of generalized biderivation. Generalizes the notion of generalized biderivation to a more general case.-
Keywords:
- Generalized biderivation.
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[1]Cheung W S.Commuting maps of triangular algebras[J].J London Math Soc, 2001, 63(1):117-127 [2]Bre\v{s}ar, M.On generalized biderivations and related maps[J].Algebra, 1995, 172(3):764-786 [3]余维燕, 张建华.三角代数上的一类非线性可交换映射[J].吉林大学学报理学版, 2014, 52(5):881-887 [4]Dominik Benkovi.Biderivations of triangular algebras[ J ][J].Linear Algebra and its Applications, 2009, 431(9):1587-1602 [5] Hou.J.-c. Generalized Jordan derivations on nest algebras[J]. Linear Algebra Appl, 2009, 430:1479-1485.[J]., 2009, 430:1479-1485 [6]Jian-Hua Zhang, Shan Feng, Hong-Xia Li, Rui-Hua Wu.Generalized biderivations of nest algebras[J][J].Linear Algebra and its Applications, 2006, 418(1):225-233 [7]Mohammad Ashraf.On generalized -biderivations in rings[J].Asian-European Journal Of Mathematics, 2011, 4(3):389-402 [8]N.RehmanOn Lie ideals and generalized Jordan left derivations of prime rings[J].Ukrainian Mathematics Journal, 2014, 65(8):1118-1125
[1]Cheung W S.Commuting maps of triangular algebras[J].J London Math Soc, 2001, 63(1):117-127 [2]Bre\v{s}ar, M.On generalized biderivations and related maps[J].Algebra, 1995, 172(3):764-786 [3]余维燕, 张建华.三角代数上的一类非线性可交换映射[J].吉林大学学报理学版, 2014, 52(5):881-887 [4]Dominik Benkovi.Biderivations of triangular algebras[ J ][J].Linear Algebra and its Applications, 2009, 431(9):1587-1602 [5] Hou.J.-c. Generalized Jordan derivations on nest algebras[J]. Linear Algebra Appl, 2009, 430:1479-1485.[J]., 2009, 430:1479-1485 [6]Jian-Hua Zhang, Shan Feng, Hong-Xia Li, Rui-Hua Wu.Generalized biderivations of nest algebras[J][J].Linear Algebra and its Applications, 2006, 418(1):225-233 [7]Mohammad Ashraf.On generalized -biderivations in rings[J].Asian-European Journal Of Mathematics, 2011, 4(3):389-402 [8]N.RehmanOn Lie ideals and generalized Jordan left derivations of prime rings[J].Ukrainian Mathematics Journal, 2014, 65(8):1118-1125
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