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

We study local generalized (α,β)-derivations on algebras generated by their idempotents and give some important applications of our results.

Abstract Regarding the question of how idempotent elements affect reversible property rings, we study a version reversibility depending on idempotents. In this perspective, introduce right (resp., left )

Let denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3, and distinct eigenvalues θ0 > θ1 > · · · > θD . Let M denote the Bose-Mesner algebra of . For 0 ≤ i ≤ D, let Ei denote the primitive idempotent of M associated with θi . We refer to E0 and ED as the trivial idempotents of M . Let E, F denote primitive idempotents of M . We say the pair E, F is taut whenever (i) E,...