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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2021 • Question 2

Question

Math 6310 • Algebra Spring 2021 • Question 2

Let \(M\) be the cokernel of the map \[ \mathbb {Z}^3\xrightarrow {\begin {pmatrix}2&2&4\\2&4&6\\2&6&8\end {pmatrix}}\mathbb {Z}^3. \]

Write \(M\) as a direct sum of cyclic \(\mathbb {Z}\)-modules.

Raw LaTeX

Let \(M\) be the cokernel of the map
\[
\mathbb{Z}^3\xrightarrow{\begin{pmatrix}2&2&4\\2&4&6\\2&6&8\end{pmatrix}}\mathbb{Z}^3.
\]

Write \(M\) as a direct sum of cyclic \(\mathbb{Z}\)-modules.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Cyclic Module Decompositions