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## Basic properties of the direct sum of groups

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.17 Solution: (1) Note that $\prod 1 \in H$, where we may take $J = \emptyset$. Thus…

## Basic properties of the countable direct sum of the integers

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.20 Let $R$ be the collection of sequences $(a_i)$ of integers, indexed by $\mathbb{N}$, such that all…