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Basic properties of the central product of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.12 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:...
The center of a direct product is the direct product of the centers
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.1 Show that ...
A finite group of width two has a trivial center
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.4 Let $G$ be...
Characterize the center of a group ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.13 Let $\mat...
Exhibit an element in the center of a group ring of finite group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.12 Let $R$ b...
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...
Basic properties of centralizers in a ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.9 Let $R$ be...
Compute the center of the Hamiltonian quaternions
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.8 Describe $...
The center of a ring is a subring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.7 The center...