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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2018 • Question 4

Question

Math 6310 • Algebra Spring 2018 • Question 4

Let \(M\) be the \(\mathbb {C}[x]\)-module generated by elements \(a,b,c\) modulo the three relations \(a+b\), \(x^3a+xb+xc\) and \((x^3+1)a+b\). Write \(M\) as a direct sum of cyclic \(\mathbb {C}[x]\)-modules.

Raw LaTeX

Let \(M\) be the \(\mathbb{C}[x]\)-module generated by elements \(a,b,c\) modulo the three relations
\(a+b\), \(x^3a+xb+xc\) and \((x^3+1)a+b\). Write \(M\) as a direct sum of cyclic
\(\mathbb{C}[x]\)-modules.

Topic Tags

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