Bulletin of the Iranian Mathematical Society, cilt.48, sa.1, ss.187-192, 2022 (SCI-Expanded)
It is shown that if A is an object in an exactly definable category C such that A has finite pure Goldie dimension and that every pure monomorphism A→ A is an isomorphism, then its endomorphism ring End C(A) is semilocal. Also, it is proved that every subobject of a pure quotient finite dimensional pure injective object of an exactly definable category has a semilocal endomorphism ring.