In the category of unital rings, there are no kernels in the category-theoretic sense; indeed, this category does not even have zero morphisms. Nevertheless, there is still a notion of kernel studied in ring theory that corresponds to kernels in the category of non-unital rings.
In the category of unital rings, there are no kernels in the category-theoretic sense; indeed this category does not even have zero morphisms. Nevertheless, there is still ,a notion of kernel studied in ring theory that corresponds to kernels in the category of non-unital rings.