Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2020, Vol. 49(1): 20-28
研究论文
三角环上的$\sigma$-双导子
$\sigma$-biderivations of Triangular Rings

袁鹤1, 李筱魁2
YUAN He1, LI Xiaokui2,*

1. 吉林师范大学数学学院, 四平, 吉林, 136000;
2. 吉林师范大学信息网络中心, 四平, 吉林, 136000
1. College of Mathematics, Jilin Normal University, Siping, Jilin, 136000, P. R. China;
2. Information and Network Center, Jilin Normal University, Siping, Jilin, 136000, P. R. China

收稿日期: 2018-11-29
出版日期: 2020-03-25
2020, Vol. 49(1): 20-28
DOI: 10.11845/sxjz.2018099b


PDF
[147 KB]
53
下载
103
浏览

引用导出
0
    /   /   推荐

摘要 本文利用极大右商环证明了一类三角环上的$\sigma$-双导子可以表示成极值$\sigma$-双导子和内$\sigma$- 双导子之和.
关键词 $\sigma$-双导子三角环极大右商环    
Abstract:In this paper, we prove that every $\sigma$-biderivation of a certain class of triangular rings is the sum of an extremal $\sigma$-biderivation and an inner $\sigma$-biderivation, using the notion of the maximal right ring of quotients.
Key words$\sigma$-biderivation    triangular ring    maximal right ring of quotients
PACS:  O153.3  
通讯作者: E-mail: *yuanhe1983@126.com   
[1] Beidar, K.I., Martindale, W.S.III and Mikhalev, A., Rings with Generalized Identities, New York: Marcel Dekker, 1996.
[2] Benkovič D.,Biderivations of triangular algebras, Linear Algebra Appl., 2009, 431(9): 1587-1602.
[3] Brešar M.,On certain pairs of functions of semiprime rings, Proc. Amer. Math. Soc., 1994, 120(3): 709-713.
[4] Brešar M.,On generalized biderivations and related maps, [J]. Algebra, 1995, 172(3): 764-786.
[5] Brešar, M., Martindale, W.S.III and Miers, C.R., Centralizing maps in prime rings with involution, [J]. Algebra, 1993, 161(2): 342-357.
[6] Cheung W.-S.,Commuting maps of triangular algebras, J. London Math. Soc. ( 2), 2001, 63(1): 117-127.
[7] Du, Y.Q. and Wang, Y., Biderivations of generalized matrix algebras, Linear Algebra Appl., 2013, 438(11): 4483-4499.
[8] Eremita D.,Functional identities of degree 2 in triangular rings, Linear Algebra Appl., 2013, 438(1): 584-597.
[9] Eremita D.,Functional identities of degree 2 in triangular rings revisited, Linear Multilinear Algebra, 2015, 63(3): 534-553.
[10] Eremita D.,Biderivations of triangular rings revisited, Bull. Malays. Math. Sci. Soc., 2017, 40(2): 505-522.
[11] Farkas, D.R. and Letzter, G., Ring theory from symplectic geometry, J. Pure Appl. Algebra, 1998, 125(1/2/3): 155-190.
[12] González C.M., Repka J. and Sánchez-Ortega J., Automorphisms $\sigma$-biderivations and $\sigma$-commuting maps of triangular algebras, Mediterr. J. Math.,2017, 14(2): Art. 68, 25 pp.
[13] Lee T.-K.,Generalized derivations of left faithful rings, Comm. Algebra, 1999, 27(8): 4057-4073.
[14] Skosyrskiǐ, V.G., Strongly prime noncommutative Jordan algebras, Trudy Inst. Mat. ( Novosibirsk), 1989, 16: 131-164, 198-199 (in Russian).
[15] Utumi Y.,On quotient rings, Osaka Math. [J]., 1956, 8: 1-18.
[16] Wang Y.,Functional identities of degree 2 in arbitrary triangular rings, Linear Algebra Appl., 2015, 479: 171-184.
[17] Wang Y.,Biderivations of triangular rings, Linear Multilinear Algebra, 2016, 64(10): 1952-1959.
[18] Yuan, H., Wang, Yao, Wang, Yu and Du, Y.Q., Strong commutativity preserving generalized derivations on triangular rings, Oper. Matrices, 2014, 8(3): 773-783.
[1] 时洪波. 单项代数的诱导代数[J]. 数学进展, 2020, 49(4): 418-428.
[2] 付艳玲, 张伟. Hilbert空间中控制对偶广义框架的刻画[J]. 数学进展, 2020, 49(3): 313-321.
[3] 崔建, 秦龙. J-clean 环的推广[J]. 数学进展, 2020, 49(1): 29-38.
[4] 时洪波. 单项代数中的循环[J]. 数学进展, 2019, 48(6): 761-765.
[5] 郭双建,王圣祥. 双 Hom 李伪超代数的构造[J]. 数学进展, 2019, 48(2): 156-170.
[6] 齐秀文,阿布都卡的·吾甫. Kauffman 代数的 Gröbner-Shirshov 基[J]. 数学进展, 2019, 48(2): 171-182.
[7] 汪力,吴俊. 一般环的广义弱 clean 指数[J]. 数学进展, 2019, 48(2): 183-190.
[8] 霍东华, 刘红玉. 对合环上可加的$\boldsymbol{k}$-$\boldsymbol{\ast}$-交换映射[J]. 数学进展, 2018, 47(3): 413-423.
[9] 欧阳伦群,周琼,刘金旺,向跃明. 强${\pi}$ nil clean 环[J]. 数学进展, 2018, 47(2): 189-200.
[10] 唐高华,吴严生,苏华东. 交换局部环上的强二和${3 \times 3}$ 矩阵[J]. 数学进展, 2018, 47(2): 182-188.
[11] 许庆兵,张孔生, 王正萍. 形式矩阵环上投射模的对偶基及其应用[J]. 数学进展, 2017, 46(4): 557-562.
[12] 陈焕银. 交换局部环上强$J$-clean矩阵[J]. 数学进展, 2017, 46(2): 212-220.
[13] 李长京, 陈全园. 环上Lie可乘映射的可加性[J]. 数学进展, 2017, 46(1): 82-90.
[14] 陈新红,卢明. 高维丛范畴中的丛倾斜对象[J]. 数学进展, 2016, 45(5): 641-651.
[15] 郭双建,王圣祥. 偏 Doi-Hopf-模上Rafael定理的应用[J]. 数学进展, 2016, 45(5): 652-664.
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .