We obtained several equivalent conditions for the existence of core inverses and dual core inverses of triangular matrices over a ring with involution. As applications, some necessary and sufficient conditions for the (2,2,0) core inverse problem are given.
Core inverse dual core inverse group inverse ring triangular matrix
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The author is grateful to China Scholarship Council for giving him a purse for his further study in Universidad Politécnica de Valencia, Spain. Research is supported by the Natural Science Foundation of Jiangsu Education Committee (No. 19KJB110005) and the Natural Science Foundation of Jiangsu Province of China (No. BK20191047).
D. S. Rakić, Nebojša Č. Dinčić, and D. S. Djordjević, Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra Appl., 463 (2014), 115–133.MathSciNetCrossRefGoogle Scholar