Generalized Biderivation Of Triangular Algebra

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.

References

[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 $(\sigma,\tau)$ -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

(σ, τ)

$(\sigma,\tau)$ -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

Generalized Biderivation Of Triangular Algebra

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