On Characterizations of Special Elements in Rings with Involution
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Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element, the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.
KeywordsMoore-Penrose inverse Core inverse EP element Star-core element Normal element Hermitian element
2000 MR Subject Classification15A09 16W10 16B99
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The authors are grateful to the referee for constructive comments towards improvement of the original version of this paper. The first author is grateful to China Scholarship Council for giving him a purse for his further study in Universidad Polit´ecnica de Valencia, Spain.