= Idempotent refinement theorem
In a finite-dimensional algebra, or a complete finite coefficient-ring algebra, primitive <idempotents> lift modulo a nilpotent <ideal> or the coefficient <maximal ideal>. Orthogonal decompositions of the identity lift, and equivalent primitive idempotents have isomorphic associated projective <modules>. Two lifts of the same idempotent modulo such an <ideal> are conjugate by a unit congruent to one. This is an <idempotent lifting> and refinement result; it does not assert that every central idempotent lifts centrally through an arbitrary nilpotent quotient.
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