arXiv subjects
Publications and source records attributed to Berke Kalebogaz.
We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate partial morphisms with (co-)phantom morphisms and injective approximations and study the existence of such approximations in these exact categories.
In this paper we study the Schröder-Bernstein problem for modules. We obtain a positive solution for the Schröder-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schröder-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their injective envelopes or pure-injective envelopes.
In this paper we study modules coinvariant under automorphisms of their projective covers. We first provide an alternative, and in fact, a more succinct and conceptual proof for the result that a module $M$ is invariant under automorphisms of its injective envelope if and only if given any submodule $N$ of $M$, any monomorphism $f:N\rightarrow M$ can be extended to an endomorphism of $M$ and then, as a dual of it, we show that over a right perfect ring, a module $M$ is coinvariant under automorphisms of its projective cover if and only if for every submodule $N$ of $M$, any epimorphism $φ: M\rightarrow M/N$ can be lifted to an endomorphism of $M$.