Further results on several types of generalized inverses

ABSTRACT

Let R be an associative ring with unity 1 and let a,b,c∈R. In this paper, several characterizations for hybrid (b,c)-inverses of a are given. Also, the hybrid (b,c)-inverse of a is characterized by the group inverse of ab, 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 (b,c)-inverses.

KEYWORDS:

• Annihilator (b,c)-inverses
• (b,c)-inverses
• double commutant properties
• hybrid (b,c)-inverses
• reverse order laws

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 15A09
• 15A27
• 16U80

Acknowledgments

The author is highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper.