Further results on several types of generalized inverses.

Let <italic>R</italic> be an associative ring with unity 1 and let <italic>a</italic>,<italic>b</italic>,<italic>c</italic>∈<italic>R</italic>. In this paper, several characterizations for hybrid (<italic>b</italic>,<italic>c</italic>)-inverses of <italic>a</italic> are given. Also, the hybrid (<italic>b</italic>,<italic>c</italic>)-inverse of <italic>a</italic> is characterized by the group inverse of <italic>ab</italic>, under certain hypothesis. In particular, existence criteria for the the inverse along an element are obtained. Finally, we get the double commutant property and the reverse order law of annihilator (<italic>b</italic>,<italic>c</italic>)-inverses. [ABSTRACT FROM AUTHOR]