If you find any mistakes, please make a comment! Thank you.

## 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: (1) Let $\pi : A \times B \rightarrow (A \times B)/Z$ denote the canonical projection,…

## Homomorphic images of ring centers are central

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.16 Solution: Suppose $r \in \varphi[Z(R)]$. Then $r = \varphi(z)$ for some $z \in Z(R)$. Now let…