Matrix Ring9

Characterize the ideals consisting of all matrices with a single nonzero column
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.1 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:...
Characterize the two-sided ideals of a matrix ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.21 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:...
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: ...
The center of a matrix ring over a commutative ring is precisely the scalar matrices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.7 Let $R$ be...
Definition and properties of matrices with a single nonzero entry
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.6 Solution: ...