Existence of Moore-Penrose inverses in rings with involution

Abstract

We give necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring with involution. If R is a ring with involution, we also investigate the existence of the Moore-Penrose inverse of the product 1 2 n x x x where 1 2 , , , n x x x are Moore-Penrose invertible elements of R .

Keywords

• Moore-Penrose inverse
• ring with involution