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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2026 • Question 1

Question

Math 6310 • Algebra Spring 2026 • Question 1

Let \(R := \mathbb {Z}\), and let \(M\) be the cokernel of the map \[ R^4 \xrightarrow { \begin {pmatrix} 2 & 7 & 3 & 4\\ 3 & 8 & 7 & 11\\ 4 & 10 & 10 & 16 \end {pmatrix} } R^3. \] Write \(M\) as a direct sum of cyclic \(R\)-modules.

Raw LaTeX

Let \(R := \mathbb{Z}\), and let \(M\) be the cokernel of the map
\[
R^4 \xrightarrow{
\begin{pmatrix}
2 & 7 & 3 & 4\\
3 & 8 & 7 & 11\\
4 & 10 & 10 & 16
\end{pmatrix}
} R^3.
\]
Write \(M\) as a direct sum of cyclic \(R\)-modules.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Cyclic Module Decompositions