On a weighted core inverse in a ring with involution |
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Authors: | Dijana Mosić Chunyuan Deng Haifeng Ma |
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Institution: | 1. Faculty of Sciences and Mathematics, University of Ni?, Ni?, Serbiadijana@pmf.ni.ac.rs;3. School of Mathematics Science, South China Normal University, Guangzhou, P. R. Chinahttps://orcid.org/0000-0002-3537-493X;4. School of Mathematics Science, Harbin Normal University, Harbin, P. R. China |
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Abstract: | We define and investigate the e-core inverse and f-dual core inverse in a ring with involution as extensions of the core and dual core inverse, respectively. Using these definitions, we present and characterize the e-core partial order and the f-dual core partial order. We describe the sets of all elements a Rickart ?-ring which are below a given element under the e-core and f-dual core partial order. New characterizations of weighted-EP elements are given too. |
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Keywords: | Core inverse core partial order dual-core inverse weighted-EP element |
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