![abstract algebra - If $1-a$ and $1-b$ are nilpotent, then show that $1-ab$ is nilpotent. - Mathematics Stack Exchange abstract algebra - If $1-a$ and $1-b$ are nilpotent, then show that $1-ab$ is nilpotent. - Mathematics Stack Exchange](https://i.stack.imgur.com/H2oUL.jpg)
abstract algebra - If $1-a$ and $1-b$ are nilpotent, then show that $1-ab$ is nilpotent. - Mathematics Stack Exchange
MATH 412 PROBLEM SET 3, SOLUTIONS Reading: • Hungerford: 14.1, and all of Chapter 3 Practice Problems: These are “easier”
![SOLVED: Q5 (2 points) Let R be a commutative ring: An element a € Ris said to be nilpotent if ak 0 for some natural number k The set I of nilpotent SOLVED: Q5 (2 points) Let R be a commutative ring: An element a € Ris said to be nilpotent if ak 0 for some natural number k The set I of nilpotent](https://cdn.numerade.com/ask_images/631c9ecc36914751acc302c26cb0a735.jpg)
SOLVED: Q5 (2 points) Let R be a commutative ring: An element a € Ris said to be nilpotent if ak 0 for some natural number k The set I of nilpotent
![SOLVED: Exercise 4. Prove that in an integral domain the zero element is the only nilpotent element: Exercise 6. Let R and S be two integral domains Show that whether the ring ( SOLVED: Exercise 4. Prove that in an integral domain the zero element is the only nilpotent element: Exercise 6. Let R and S be two integral domains Show that whether the ring (](https://cdn.numerade.com/ask_images/ee26867179a04738b4f3af5cdf4537aa.jpg)