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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2023 • Question 5

Question

Math 6310 • Algebra Fall 2023 • Question 5

Find four non-isomorphic \(\mathbb {Z}\)-modules (i.e. abelian groups) \(M\) that each fit into an exact sequence of the form:

\[ 0\to \mathbb {Z}\to M\to \mathbb {Z}/6\mathbb {Z}\to 0 \]

Raw LaTeX

Find four non-isomorphic \(\mathbb{Z}\)-modules (i.e. abelian groups) \(M\) that each fit into an exact sequence of the form:

\[
0\to\mathbb{Z}\to M\to\mathbb{Z}/6\mathbb{Z}\to0
\]

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Chinese Remainder Theorem and Product Decompositions Exact Sequences of Modules