The German term Rektion derives from Latin casus rectus, which is the basic case, the nominative form. Rektion addresses two questions:
1.) when does an adjective get declined; and,
2.) what is its ending when it does?
Let us examine the topic in the view of syntax logic. It is Rektion that enables a preceding preposition to govern the declension case, thus narrowing the definition of the associated Satzglied. Satzglied is any of the phrase's word groups other than subject and predicate. The following frequently used prepositions are thus listed under the name of the case they demand (i.e. govern). By definition, no preposition governs casus rectus.
Accusative
ab, bis, durch, entlang, für, gegen, ohne, um, wider
Examples: Er fährt ohne sie. Für Bargeld. Er handelt wider alle Vernunft.
In addition, die direction-defining prepositions govern the accusative. See the following Sec. "Dative."
Dative
an, auf, aus, hinter, in, neben, über, unter, vor, zwischen
Note: The dative case is governed only when a locality is defined. Test question: "wo?" (wher?). When a direction is being defined, the accusative case is governed. Test question: "wohin?" (whither?)
Examples: aus dem Fenster (winken). An die Einfahrt (herfahren).
Genitiveabseits, anläßlich, anstatt, anstelle, aufgrund, außerhalb, diesseits, infolge, inmitten, innerhalb, jenseits, kraft, mittels, oberhalb, seitens, statt, ungeachtet, unterhalb, unweit, vermittels, während, wegen, zufolge
Example: Wegen des Unfalls
Declension Criteria (i.e. when are adjectives declined, and when not?)
Adjectives must be declined when
used as noun attribute before a noun: ein wichtiges Gespräch. See the tables in the paragraph following!
used as noun: das Schwarze. That is substantiviertes Adjektiv (adjective used as noun).
Adjectives remain undeclined when used
as phrase adjective - that is either as predicative: (Sie ist gut. Das ist falsch), or adverbially (Sie arbeitet schwer)
as attribute of an adjective or adverb: Ein grässlich kalter Wind weht heute. Die Burg liegt hoch oben. However, compare this to parallel declension. See that Section, below.