Some relations about the generalizations of self-injective ring: P-injective ring, GP-injective ring, AP-injective ring, simple-injective ring and n-injective ring are studied.
Let A be a finite-dimensional algebra over arbitrary base fieldk. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensionalk-algebras B and C: then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):
