Ring Homomorphism13

Ring homomorphisms preserve nilpotency
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.32 Solution:...
The ring homomorphic image of an ideal is an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.24 Solution:...
Ring homomorphisms map an identity element to an identity or a zero divisor
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.17 Solution:...
Homomorphic images of ring centers are central
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.16 Solution:...
Embed the Hamiltonian quaternions in a ring of real matrices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.14 Solution:...
Embed the complex numbers in a ring of real matrices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.13 Solution:...
Embed a ring of quadratic integers in a ring of matrices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.12 Solution:...
Exhibit a mapping which is a group homomorphism but not a ring homomorphism
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.11 Solution:...
Prove that a given function is a ring homomorphism and describe its kernel
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.7 Solution: ...
Determine whether or not a mapping is a ring homomorphism
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.6 Decide whi...