J. Austral. Math. Soc.
72 (2002), 137-152
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Elements of rings with equal spectral idempotents
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J. J. Koliha
Department of Mathematics and Statistics
University of Melbourne
VIC 3010
Australia
koliha@unimelb.edu.au
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and
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Pedro Patricio
CMAT - Centro de Matemática
Universidade do Minho
4710-057 Braga
Portugal
pedro@math.uminho.pt
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Abstract
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In this paper we define and study a generalized
Drazin inverse xD
for ring elements x, and give a characterization of elements
a, b for which
a aD = b bD.
We apply our results to the study of EP elements in a ring with involution.
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