A ring is called Boolean if for all . Prove that every Boolean ring is commutative.
Note first that for all , . Now if , we have . Thus , and we have . But then . Thus is commutative.
A ring is called Boolean if for all . Prove that every Boolean ring is commutative.
Note first that for all , . Now if , we have . Thus , and we have . But then . Thus is commutative.
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.