For ⋀ a finite dimensional local algebra with radicalNwhereNn= 0 ≠Nn-1define(as a right A-module), thenA(⋀) is quasi-hereditary and it has a unique heredity idealJ1(A).Assume ⋀ satisfies the right socle condition (the socle series and the radical series of ⋀⋀coincide). We show that then the algebraAi/J1(Ai-1) is isomorphic toAi-1whereAi=A(⋀/Ni). for 1 ≤ i ≤ n. Moreover we determine the canonical module forA(⋀) and we show that the Ringel dual ofA(⋀) is isomorphic to the endomorphism ring ofas a left module, provided that ⋀ also satisfies the left socle condition.