Nilpotent11

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:...
An ideal which is finitely generated by nilpotent elements is nilpotent
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.28 Solution:...
Constructing units from nilpotent elements in a commutative ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.27 Solution:...
Basic properties of quotients of a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.14 Solution:...
An example of a nilpotent ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.37 Solution:...
Characterize the units and nilpotent elements of a polynomial ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.33 Solution:...
Ring homomorphisms preserve nilpotency
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.32 Solution:...
In a noncommutative ring, the set of nilpotent elements need not be an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.31 Solution:...
The set of nilpotent elements in a commutative ring is an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.29 Solution:...
Basic properties of nilpotent ring elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.14 Let $R$ b...