| Popis: |
Let \(\mathfrak{C}\) be a category. An objet A in \(\mathfrak{C}\) is said to be mono-correct (respectively epi-correct) if for any B in \(\mathfrak{C}\), and f: A ⟶ B, g: B ⟶ A two monomorphisms (respectively epimorphisms) then A ≃ B. In category Set, this property is known as the Cantor Bernstein theorem and it’s dual. In category of abelian groups, we show that the Cantor Bernstein theorem is not verified. In R-mod, we study some relations between mono-correctness of modules and some algebraic operations as for submodules, direct sum of modules and factor modules. |
