On the Algebraic Characterizations of Right Invertible Operators of Higher Degree

Abstract

Abstract. This paper proves some algebraic charaterizations and Volterra characterizations of the generalized right invertible operators of degree k in the case of k > 2. A class of equations induced by generalized right invertible operators of degree of k can be solved in a closed form.

On the solvability of systems of linear equations on commutative semigroup

“…The set of all generalized invertible operators will be denoted by W(S). Let W A denote the set of all generalized inverses of an operator A ∈ W(S) (see [5,6]). …”