The lemma motivates our calling R a generalized Picard group.
It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.
Whether or not this is correct does not matter; we are trying to motivate the proof that follows.
The following theorem is clearly motivated by the classical LP-decomposition.
The present paper is motivated by the desire to make the subject as accessible as possible.
Motivated by (4), we obtain the following characterization of......
This motivated the second author to introduce the notion of......