![SOLVED: An element x in a ring is nilpotent if xn = 0 for some integer n. Find all nilpotent elements in the rings Z/Z30 and Z/Z40 SOLVED: An element x in a ring is nilpotent if xn = 0 for some integer n. Find all nilpotent elements in the rings Z/Z30 and Z/Z40](https://cdn.numerade.com/ask_previews/0a99fed2-7483-4faf-aa42-9b6a8ab33199_large.jpg)
SOLVED: An element x in a ring is nilpotent if xn = 0 for some integer n. Find all nilpotent elements in the rings Z/Z30 and Z/Z40
MATH 412 PROBLEM SET 3, SOLUTIONS Reading: • Hungerford: 14.1, and all of Chapter 3 Practice Problems: These are “easier”
![SOLVED: Exercise % Nilpotent elements 80 pts) Let R be commutative ring: We say that element € R is nilpotent if there exists an integer such that 0. We write Nil( R) SOLVED: Exercise % Nilpotent elements 80 pts) Let R be commutative ring: We say that element € R is nilpotent if there exists an integer such that 0. We write Nil( R)](https://cdn.numerade.com/ask_images/6e6a07770bf64ae9bf5759b21a418c83.jpg)
SOLVED: Exercise % Nilpotent elements 80 pts) Let R be commutative ring: We say that element € R is nilpotent if there exists an integer such that 0. We write Nil( R)
![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)