M. K. Berktas, S. Crivei: On complete pure-injectivity, p. 331-337


Let $\mathcal{C}$ be a locally finitely presented additive category, and let $E$ be a finitely presented pure-injective object of $\mathcal{C}$. We prove that $E$ has an indecomposable decomposition if and only if every pure epimorphic image of $E$ is pure-injective if and only if the endomorphism ring of $E$ is semiperfect. This extends a module-theoretic result which generalises the classical Osofsky Theorem.

Key Words: Locally finitely presented category, Krull-Schmidt category, indecomposable decomposition, (completely) pure-injective object, semiperfect ring, semisimple ring, Osofsky theorem.

2010 Mathematics Subject Classification: Primary 18E05,
Secondary 18C35, 16D90.