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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2014 • Question 3

Question

Math 6310 • Algebra Spring 2014 • Question 3

Let \(M\) be the cokernel of the map \(\mathbb {Z}^2\longrightarrow \mathbb {Z}^3\) given by \[ \begin {pmatrix} 3 & 6\\ 4 & 10\\ 10 & 22 \end {pmatrix}. \] Write \(M\) as a direct sum of cyclic groups.

Raw LaTeX

Let \(M\) be the cokernel of the map \(\mathbb{Z}^2\longrightarrow\mathbb{Z}^3\) given by
\[
\begin{pmatrix}
3 & 6\\
4 & 10\\
10 & 22
\end{pmatrix}.
\]
Write \(M\) as a direct sum of cyclic groups.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Cyclic Module Decompositions