Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 139 / 2 / a / Solution

Schur lemma says that a homomorphism between simple modules is either zero or an isomorphism; consequently the endomorphism ring of a simple module is a division ring. Indeed, the kernel and image of a module homomorphism are submodules. Simplicity makes each either zero or the whole module, proving both assertions.

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