New characterizations of EP, generalized normal and generalized Hermitian elements in rings |
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| Authors: | Dijana Mosi? Dragan S. Djordjevi? |
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| Affiliation: | Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia |
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| Abstract: | We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy ana∗ = a∗an or an = (a∗)n for arbitrary n ∈ N. For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution. |
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| Keywords: | EP elements Moore-Penrose inverse Group inverse Generalized normal elements Generalized Hermitian elements Ring with involution |
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