Drazin–Moore–Penrose invertibility in rings

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Characterizations of core and dual core inverses in rings with involution (2016, background): “They also called a ∗-gMP invertible if a is both Moore–Penrose invertible and group invertible with a† = a# in [2].”
Pseudo core inverses in rings with involution (2016, background): “The sum a = ca+na is called the core nilpotent decomposition [14] of a, where ca = aa a is the core part of a, and na = (1− aa )a is the nilpotent part of a.”
Generalized inverses modulo ℋ in semigroups and rings (2013, background): “We get u ∗ = a ∗ a + 1 − aa − is a unit, which is the classical relation [13].”
On generalized inverses and Green's relations (2009, background): “Combining theorem 4 and theorem 9, we then get directly the following existence criteria and commuting relations for the classical inverses [6], [3], [7], [8], [9], [10], [13]:”
EP elements in rings (2009, unknown): “Patŕıcio and Puystjens in [22] further discuss the necessary and sufficient conditions for a regular element a to be EP.”