On objects with a semilocal endomorphism rings in finitely accessible additive categories (Q895863)

It is well known that objects with semilocal endomorphism rings have interesting and useful properties (e.g. they have the cancellation property). In the present paper the authors prove that if \(A\) is an object in a finitely accessible additive category \(\mathcal{A}\) such that it has finite pure Goldie dimension and that every pure mono endomorphism of \(A\) is an isomorphism, then the endomorphism ring of A is semilocal (Theorem 5).