您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 97-105.doi: 10.6040/j.issn.1671-9352.0.2021.247

• • 上一篇    

广义矩阵代数上一类非全局非线性三重高阶可导映射

费秀海,张海芳*   

  1. 滇西科技师范学院数理学院, 云南 临沧 677099
  • 发布日期:2022-10-06
  • 作者简介:费秀海(1980— ),男,博士,教授,研究方向为算子代数与算子理论.E-mail: xiuhaifei@snnu.edu.cn*通信作者简介:张海芳(1980— ),女,硕士,教授,研究方向为算子代数与算子理论.E-mail: zhanghaifang103427@yeah.net
  • 基金资助:
    国家自然科学基金资助项目(11901248);云南省教育厅基础研究基金资助项目(2022J1014);云南省2021年学术和技术后备带头人才资助项目(202105AC160089)

A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras

FEI Xiu-hai, ZHANG Hai-fang*   

  1. School of Mathematics and Physics, West Yunnan University, Lincang 677099, Yunnan, China
  • Published:2022-10-06

摘要: 设G是一个满足MN=0=NM的2-无挠的广义矩阵代数,Q={A∈G:A2=0},D={dn}n∈N是G上一列映射(没有可加性假设)。文章证明:若对任意n∈N,A,B,C∈G且ABC∈Q,有dn(ABC)=∑r+s+t=ndr(A)ds(B)dt(C),则D是一个可加的高阶导子。作为应用,在三角代数上得到了相同的结论。

关键词: 广义矩阵代数, 三重高阶可导映射, 高阶导子

Abstract: Let G be a 2-torsion free generalized matrix algebra with MN=0=NM,Q={A∈G:A2=0} and D={dn}n∈N be a sequence mapping from G into itself(without assumption of additivity). In this paper, it is shown that if D satisfies dn(ABC)=∑r+s+t=ndr(A)ds(B)dt(C)for all n∈N,A,B,C∈G with ABC∈Q, then D is an additive higher derivation. As its applications get that the similar conclusion on Triangular algebras.

Key words: generalized matrix algebra, triple higher derivable map, higher derivation

中图分类号: 

  • O177.1
[1] HERSTEIN I N. Jordan derivations of prime rings[J]. Proc Amer Math Soc, 1957, 8(6):1104-1110.
[2] BREVSAR M, VUKMAN J. Jordan derivations on prime rings[J]. Bull Austral Math Soc, 1988, 37(3):321-322.
[3] ZHANG Jianhua, YU Weiyan. Jordan derivations of triangular algebras[J]. Linear Algebra Appl, 2006, 419(1):251-255.
[4] LU Fangyan. Jordan derivable maps of prime rings[J].Comm Algebra, 2010, 38(12):4430-4440.
[5] ASHRAF M, JABEEN A. Nonlinear Jordan triple derivable mappings of triangular algebras[J]. Pac J Appl Math, 2016, 7(4):229-239.
[6] LI Jiankui, PAN Zhidong, SEHN Qihua. Jordan and Jordan higher all-derivable points of some algebras[J]. Linear and Multilinear Algebra, 2013, 61(6):831-845.
[7] ZHAO Jingping, ZHU Jun. Jordan higher all-derivable points in triangular algebras[J]. Linear Algebra Appl, 2012, 436(9):3072-3086.
[8] XIAO Zhankui, WEI Feng. Jordan higher derivations on triangular algebras[J]. Linear Algebra Appl, 2010, 432(10):2615-2622.
[9] LIU Dan, ZHANG Jianhua. Jordan higher derivable maps on triangular algebras by commutative zero products[J]. Acta Math Sinica(English Series), 2016, 32(2):258-264.
[10] HUANG Wenbo, LI Jiankui, HE Jun. Characterizations of Jordan mappings on some rings and algebras through zero products [J]. Linear and Multilinear Algebra, 2017, 60(2):167-180.
[11] ASHRAF M, JABEEN A. Nonlinear Jordan triple higher derivable mappings of triangular algebras[J]. Southeast Asian Bull Math, 2018, 42(4):503-520.
[12] FU Wenlian, XIAO Zhankui, DU Xiankun. Nonlinear Jordan higher derivations on triangular algebras[J]. Communications in Mathematical Research, 2015, 31(2):119-130.
[13] WONG Dein, MA Xiaobin, CHEN Li. Nonlinear mappings on upper triangular matrices derivable at zero point[J]. Linear Algebra Appl, 2015, 483(5):236-248.
[14] WANG Long. Nonlinear mappings on full matrices derivable at zero point[J]. Linear and Multilinear Algebra, 2016, 65(11):725-730.
[15] 孟利花,张建华.三角代数上的一类非全局三重可导映射[J].数学学报(中文版), 2017, 60(6):955-960. MENG Lihua, ZHANG Jianhua. A class non-global triple derivable maps on triangular algebras[J]. Acta Math Sinica, 2017, 60(6):955-960.
[16] 费秀海,戴磊,朱国位.广义矩阵代数上的一类局部非线性三重可导映射[J].浙江大学学报(理学版), 2020, 47(2):167-171. FEI Xiuhai, DAI Lei, ZHU Guowei. A class local nonlinear triple derivable maps on generalized matrix algebras[J]. Journal of Zhejiang University(Science Edition), 2020, 47(2):167-171.
[17] SANDS A D. Radicals and morita contexts[J]. Journal of Algebra, 1973, 24(2):335-345.
[18] CHEUNG W S. Mappings on triangular algebras[D]. Victoria, Canada: University of Victoria, 2000.
[1] 马帅英,张建华. 三角代数上的一类非全局高阶可导非线性映射[J]. 《山东大学学报(理学版)》, 2021, 56(2): 48-55.
[2] 费秀海,戴磊,朱国卫. 三角代数上Lie积为平方零元的非线性Jordan高阶可导映射[J]. 《山东大学学报(理学版)》, 2019, 54(12): 50-58.
[3] 费秀海,戴磊. 广义矩阵代数上双可导映射的可加性[J]. 《山东大学学报(理学版)》, 2019, 54(10): 85-90.
[4] 张霞,张建华. 三角代数上互逆元处的高阶ξ-Lie可导映射[J]. 《山东大学学报(理学版)》, 2019, 54(10): 79-84.
[5] 张芳娟. 广义矩阵代数上的非线性Lie中心化子[J]. 山东大学学报(理学版), 2015, 50(12): 10-14.
[6] 胡丽霞,张建华. 三角代数上的零点Lie高阶可导映射[J]. J4, 2013, 48(4): 5-9.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!