  The Jones-Wenzl idempotents of the Temperley-Lieb algebra are celebrated
elements defined over characteristic zero and for generic loop parameter. Given
pointed field $(R, \delta)$, we extend the existing results of Burrull,
Libedinsky and Sentinelli to determine a recursive form for the idempotents
describing the projective cover of the trivial $TL_n^R(\delta)$-module.
