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 - 2018, Vol. 47(2): 182-188
 研究论文
 交换局部环上的强二和${3 \times 3}$ 矩阵 Strong 2-sum ${3\times 3}$ Matrices over Commutative Local Rings 唐高华1,2,吴严生1,3,苏华东1 TANG Gaohua1,2, WU Yansheng1,3,*, SU Huadong1 1. 广西师范学院数学与统计科学学院, 南宁, 广西, 530023; 2. 钦州学院, 钦州, 广西, 535011; 3. 南京航空航天大学理学院, 南京, 江苏, 210016 1. School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China; 2. Qinzhou University, Qinzhou, Guangxi, 535011, P. R. China; 3. School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, P. R. China 收稿日期: 2016-05-25 出版日期: 2018-05-16 2018, Vol. 47(2): 182-188 DOI: 10.11845/sxjz.2016068b
 249 浏览 引用导出
0
/   /   推荐

Abstract：An element of a ring $R$ is called to have the strong 2-sum property if it is a sum of two units that commute with each other. And a ring $R$ is called a strong 2-sum ring if every element of $R$ has the strong 2-sum property. In this paper, we investigate the strong 2-sum property of two subrings, $\mathcal{L}(R)$ and $\mathfrak{L}(R)$, of $3 \times 3$ matrix rings over commutative local rings. We prove that for a commutative local ring $R$, $\mathcal{L}(R)$ is a strong 2-sum ring if and only if $R$ is a strong 2-sum ring if and only if $\mathfrak{L}(R)$ is a strong 2-sum ring. Moreover, we prove that for a commutative local ring $R$, it is a strong 2-sum ring if and only if every corner ring of $\mathbb{T}_n(R) (n=2,3)$ is a strong $2$-sum ring.
Key wordsstrong 2-sum ring    $3\times 3$ matrix ring    local ring    corner ring
 PACS: O153.3
 [1] Cui, J. and Chen, J.L., Strongly clean $3\times 3$ matrices over a class of local rings, J. Nanjing Univ. (Math. Biquarterly), 2010, 27(1): 31-40.[2] Gurgun, O., Halicioglu, S. and Harmanci, A., Quasipolar subrings of $3 \times 3$ matrix rings, An. St. Univ. Ovidius Constanta, 2013, 21(3): 133-146.[3] Tang, G.H., Wu, Y.S., Li, Y. and Zhang, H.B., Strong 2-sum property of local rings and their extensions, J. Guangxi Norm. Univ. Nat. Sci. Ed., 2016, 34(1): 72-77 (in Chinese).[4] Tang, G.H. and Zhou, Y.Q., When is every linear transformation a sum of two commuting invertible ones? Linear Algebra Appl., 2013, 439(11): 3615-3619.[5] Tang, G.H. and Zhou, Y.Q., An embedding theorem on triangular matrix rings, Linear Multilinear Algebra, 2017, 65(7): 882-890.[6] Vàmos, P., 2-good rings, Q. J. Math., 2005, 56(3): 417-430.[7] Wolfson, K.G., An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math., 1953, 75(2): 353-386.[8] Zelinsky, D., Every linear transformation is a sum of nonsingular ones,Proc. Amer. Math. Soc., 1954, 5(4): 627-630.
 [1] 汪慧星. 强拟诣零clean环[J]. 数学进展, 2019, 48(1): 53-60. [2] 陈焕银. 交换局部环上强$J$-clean矩阵[J]. 数学进展, 2017, 46(2): 212-220. [3] 周美秀;潜陈印;蒋忠樟;. p(x)-Laplacian Neumann问题的解与多解(英文)[J]. 数学进展, 2010, 39(3): 361-374. [4] 李宝毅,张芷芬. 平面可积系统的多角环S~(2)在小扰动下的环性(英文)[J]. 数学进展, 1999, 28(1): 29-40.
Viewed
Full text

Abstract

Cited

Discussed