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Let      A \mathfrak {A}       be a generalized Hilbert algebra and let      J \mathcal {J}       be a closed right ideal of      A \mathfrak {A}      . Let      J ⊥  {\mathcal {J}^ \bot }       denote the pre-Hilbert space orthogonal complement of      J \mathcal {J}       in      A \mathfrak {A}      . The problem investigated in this paper is: for which algebras      A \mathfrak {A}       is it true that      A = J ⊕  J ⊥  \mathfrak {A} = \mathcal {J} \oplus {\mathcal {J}^ \bot }       for every closed right ideal      J \mathcal {J}       of      A \mathfrak {A}      ? In the case that      A \mathfrak {A}       is achieved, a slightly stronger property is characterized and these characterizations are then used to investigate some interesting examples.

Complementation for right ideals in generalized Hilbert algebras