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Properties of core-EP order in rings with involution. (English) Zbl 1473.15008

Summary: 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 \(n \times n\) complex matrices [Linear Algebra Appl. 508, 289–300 (2016; Zbl 1346.15003)] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Y. Gao et al., Filomat 32, No. 9, 3073–3085 (2018; doi:10.2298/fil1809073g)]. 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.

MSC:

15A09 Theory of matrix inversion and generalized inverses
06A06 Partial orders, general
16W10 Rings with involution; Lie, Jordan and other nonassociative structures

Citations:

Zbl 1346.15003
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References:

[1] Baksalary O M, Trenkler G. Core inverse of matrices. Linear Multilinear Algebra, 2010, 58(6): 681-697 · Zbl 1202.15009 · doi:10.1080/03081080902778222
[2] Campbell S L, Meyer C D. Generalized Inverse of Linear Transformations. Classics Appl Math, Vol 56. Philadelphia: SIAM, 2009 · Zbl 1158.15301
[3] Drazin M P. Pseudo-inverse in associative rings and semigroups. Amer Math Monthly, 1958, 65: 506-514 · Zbl 0083.02901 · doi:10.1080/00029890.1958.11991949
[4] Gao Y, Chen J. Pseudo core inverses in rings with involution. Comm Algebra, 2018, 46(1): 38-50 · Zbl 1392.15005 · doi:10.1080/00927872.2016.1260729
[5] Gao Y, Chen J, Ke Y. *-DMP elements in *-semigroups and *-rings. Filomat, 2018, 32: 3073-3085 · Zbl 1513.16067 · doi:10.2298/FIL1809073G
[6] Harte R, Mbekhta M. On generalized inverses in C*-algebras. Studia Math, 1992, 103(1): 71-77 · Zbl 0810.46062 · doi:10.4064/sm-103-1-71-77
[7] Hartwig R E, Levine J. Applications of the Drazin inverse to the Hill cryptographic system, Part III. Cryptologia, 1981, 5(2): 67-77 · Zbl 0491.94015 · doi:10.1080/0161-118191855850
[8] Manjunatha Prasad K, Mohana K S. Core-EP inverse. Linear Multilinear Algebra, 2014, 62(6): 792-802 · Zbl 1306.15006 · doi:10.1080/03081087.2013.791690
[9] Marovt J. Orders in rings based on the core-nilpotent decomposition. Linear Multilinear Algebra, 2018, 66(4): 803-820 · Zbl 1469.06022 · doi:10.1080/03081087.2017.1323846
[10] Miller V A, Neumann M. Successive overrelaxation methods for solving the rank deficient linear least squares problem. Linear Algebra Appl, 1987, 88-89: 533-557 · Zbl 0624.65033 · doi:10.1016/0024-3795(87)90124-8
[11] Mitra S K, Bhimasankaram P, Malik S B. Matrix Partial Orders, Shorted Operators and Applications. Series in Algebra, Vol 10. London: World Scientific, 2010 · Zbl 1203.15023
[12] Rakić D S, Dinčić N Č; Djordjević D S. Group, Moore-Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl, 2014, 463: 115-133 · Zbl 1297.15006 · doi:10.1016/j.laa.2014.09.003
[13] Rakić D S, Djordjević D S. Star, sharp, core and dual core partial order in rings with involution. Appl Math Comput, 2015, 259: 800-818 · Zbl 1391.16044
[14] Rao C R, Mitra S K. Generalized Inverse of Matrices and Its Application. New York: Wiley, 1971 · Zbl 0236.15004
[15] Wang H. Core-EP decomposition and its applications. Linear Algebra Appl, 2016, 508: 289-300 · Zbl 1346.15003 · doi:10.1016/j.laa.2016.08.008
[16] Xu S, Chen J, Zhang X. New characterizations for core inverses in rings with involution. Front Math China, 2017, 12(1): 231-246 · Zbl 1379.16029 · doi:10.1007/s11464-016-0591-2
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