## Prove that the augmentation ideal of a given group ring is nilpotent

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.29 Solution: We begin with some lemmas. Lemma 1: Let $\pi : G \rightarrow H$ be a…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.2 Solution: Recall that the augmentation ideal of $R[G]$ is the kernel of the ring homomorphism $R[G]…