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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2018 • Question 3

Question

Math 6310 • Algebra Summer 2018 • Question 3

Suppose that \(R=\mathbb {C}[x]\), and that \(M\) is the \(R\)-module generated by three elements \(a,b\), and \(c\), modulo the three relations \(a-xc\), \(xa-xb+xc\), and \(xb-(x^2-1)c\). Write \(M\) as a direct sum of cyclic modules.

Raw LaTeX

Suppose that \(R=\mathbb{C}[x]\), and that \(M\) is the \(R\)-module generated by three elements
\(a,b\), and \(c\), modulo the three relations \(a-xc\), \(xa-xb+xc\), and \(xb-(x^2-1)c\). Write
\(M\) as a direct sum of cyclic modules.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Cyclic Module Decompositions Modules over PIDs