Properties of core-EP order in rings with involution

doi:10.1007/s11464-019-0782-8

Front. Math. China

2019, Vol. 14

Issue (4) : 715-736 https://doi.org/10.1007/s11464-019-0782-8

RESEARCH ARTICLE

Properties of core-EP order in rings with involution

Gregor DOLINAR^1,⁴, Bojan KUZMA^2,⁴, Janko MAROVT^3,⁴(

), Burcu UNGOR⁵

¹. University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, SI-1000 Ljubljana, Slovenia
². University of Primorska, Glagoljaska 8, SI-6000 Koper, Slovenia
³. University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia
⁴. IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia
⁵. Faculty of Sciences, Ankara University, 06100, Tandogan, Ankara, Turkey

Download: PDF(295 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289–300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073–3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in-rings.

Keywords Drazin inverse core-EP decomposition pre-order ring

Corresponding Author(s): Janko MAROVT

Issue Date: 23 September 2019

Cite this article:

Gregor DOLINAR,Bojan KUZMA,Janko MAROVT, et al. Properties of core-EP order in rings with involution[J]. Front. Math. China, 2019, 14(4): 715-736.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0782-8
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I4/715

1	O M Baksalary, G Trenkler. Core inverse of matrices. Linear Multilinear Algebra, 2010, 58(6): 681–697 https://doi.org/10.1080/03081080902778222
2	S L Campbell, C D Meyer. Generalized Inverse of Linear Transformations. Classics Appl Math, Vol 56. Philadelphia: SIAM, 2009 https://doi.org/10.1137/1.9780898719048
3	M P Drazin. Pseudo-inverse in associative rings and semigroups. Amer Math Monthly, 1958, 65: 506–514 https://doi.org/10.1080/00029890.1958.11991949
4	Y Gao, J Chen. Pseudo core inverses in rings with involution. Comm Algebra, 2018, 46(1): 38–50 https://doi.org/10.1080/00927872.2016.1260729
5	Y Gao, J Chen, Y Ke. -DMP elements in-semigroups and -rings. Filomat, 2018, 32: 3073–3085 https://doi.org/10.2298/FIL1809073G
6	R Harte, M Mbekhta. On generalized inverses in C*-algebras. Studia Math, 1992, 103(1): 71–77 https://doi.org/10.4064/sm-103-1-71-77
7	R E Hartwig, J Levine. Applications of the Drazin inverse to the Hill cryptographic system, Part III. Cryptologia, 1981, 5(2): 67–77 https://doi.org/10.1080/0161-118191855850
8	K Manjunatha Prasad, K S Mohana. Core-EP inverse. Linear Multilinear Algebra, 2014, 62(6): 792–802 https://doi.org/10.1080/03081087.2013.791690
9	J Marovt. Orders in rings based on the core-nilpotent decomposition. Linear Multi-linear Algebra, 2018, 66(4): 803–820 https://doi.org/10.1080/03081087.2017.1323846
10	V A Miller, M Neumann. Successive overrelaxation methods for solving the rank deficient linear least squares problem. Linear Algebra Appl, 1987, 88-89: 533–557 https://doi.org/10.1016/0024-3795(87)90124-8
11	S K Mitra, P Bhimasankaram, S B Malik. Matrix Partial Orders, Shorted Operators and Applications. Series in Algebra, Vol 10. London: World Scientific, 2010 https://doi.org/10.1142/9789812838452
12	D S Rakić, N Č Dinčić, D S Djordjević. Group, Moore-Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl, 2014, 463: 115–133 https://doi.org/10.1016/j.laa.2014.09.003
13	D S Rakić, D S Djordjević. Star, sharp, core and dual core partial order in rings with involution. Appl Math Comput, 2015, 259: 800–818 https://doi.org/10.1016/j.amc.2015.02.062
14	C R Rao, S K Mitra. Generalized Inverse of Matrices and Its Application. New York: Wiley, 1971
15	H Wang. Core-EP decomposition and its applications. Linear Algebra Appl, 2016, 508: 289–300 https://doi.org/10.1016/j.laa.2016.08.008
16	S Xu, J Chen, X Zhang. New characterizations for core inverses in rings with involution. Front Math China, 2017, 12(1): 231–246 https://doi.org/10.1007/s11464-016-0591-2

[1]	Meiqi YAN, Hailou YAO. Pure projective modules and FP-injective modules over Morita rings[J]. Front. Math. China, 2020, 15(6): 1265-1293.
[2]	Dijana MOSIC, Daochang ZHANG. Weighted weak group inverse for Hilbert space operators[J]. Front. Math. China, 2020, 15(4): 709-726.
[3]	Yuefeng GAO, Jianlong CHEN, Pedro PATR_ICIO. Weighted binary relations involving core-EP inverse[J]. Front. Math. China, 2020, 15(4): 685-699.
[4]	Tianyi ZHONG, Yilan TAN. On B₆- and B₇-groups[J]. Front. Math. China, 2020, 15(3): 613-616.
[5]	Fanghui LIAO, Zhengyang LI. Hardy space estimates for bi-parameter Littlewood-Paley square functions[J]. Front. Math. China, 2020, 15(2): 333-349.
[6]	Hongzhi HUANG. Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry[J]. Front. Math. China, 2020, 15(1): 69-89.
[7]	Junyi ZHU, Xinxin MA, Zhijun QIAO. Spectral analysis of generalized Volterra equation[J]. Front. Math. China, 2019, 14(5): 1063-1075.
[8]	Rui ZHANG. Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes[J]. Front. Math. China, 2019, 14(5): 1017-1035.
[9]	Ziqiu LIU, Yunfeng ZHAO, Yuqin ZHANG. Perfect 3-colorings on 6-regular graphs of order 9[J]. Front. Math. China, 2019, 14(3): 605-618.
[10]	Sanzheng QIAO, Yimin WEI. Acute perturbation of Drazin inverse and oblique projectors[J]. Front. Math. China, 2018, 13(6): 1427-1445.
[11]	Chengtao YUAN, Ruju ZHAO, Libin LI. Irreducible $ℤ +$ -modules of near-group fusion ring K( $ℤ 3$ , 3)[J]. Front. Math. China, 2018, 13(4): 947-966.
[12]	Gaiyun GAO, Zhixin LIU. Results of Diophantine approximation by unlike powers of primes[J]. Front. Math. China, 2018, 13(4): 797-808.
[13]	Tai Keun KWAK, Yang LEE, Young Joo SEO. Some remarks on one-sided regularity[J]. Front. Math. China, 2018, 13(4): 833-847.
[14]	Hao WEN. Asymptotic estimate of a twisted Cauchy-Riemann operator with Neumann boundary condition[J]. Front. Math. China, 2017, 12(6): 1469-1481.
[15]	Hongjie SONG, Changqing XU. Neighbor sum distinguishing total chromatic number of K₄-minor free graph[J]. Front. Math. China, 2017, 12(4): 937-947.

Viewed

Full text

Abstract

Cited

Shared

Discussed