Let be a principal ideal domain and let be a torsion -module. Prove that the -primary component of is a submodule for every prime . Prove that is the direct sum of its -primary components.
We proved this in a previous exercise.
Let be a principal ideal domain and let be a torsion -module. Prove that the -primary component of is a submodule for every prime . Prove that is the direct sum of its -primary components.
We proved this in a previous exercise.
On these pages you will find a slowly growing (and poorly organized) list of proofs and examples in abstract algebra.
No doubt these pages are riddled with typos and errors in logic, and in many cases alternate strategies abound. When you find an error, or if anything is unclear, let me know and I will fix it.