diminutions: embellishments
Embellishments are created by involving the notes surrounding chord tones. The example below from Czerny's Pianoforte-Schule Op.500 (1839) shows a broken C chord embellished using the semitones below the chord tones.
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Often the diatonic note above the chord tone is included as well, as shown in the example below from Montgeroult's Cours complet pour l'enseignement du forte piano (composed 1788-1812).
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An infinite number of combinations can be made with embellishing tones. Despite the fact that embellishing tones in arpeggios are very often found in written-out preludes, piano methods rarely provide specific exercises for this. However, one may find examples where semitones are added in a scale exercise, as in the example below from Adam's Encyclopédie du Pianiste Compositeur (1840).
Some examples for studying common embellishment patterns on a C chord can be found here.