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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2019 • Question 7

Question

Math 6310 • Algebra Spring 2019 • Question 7

Let \(R=\mathbb {Q}[x]\) and consider the submodule \(M\) of \(R^2\) generated by the elements \((x^2-1,x-1)\) and \((x^2+x,x)\). Write \(M\) as a direct sum of cyclic modules.

Raw LaTeX

Let \(R=\mathbb{Q}[x]\) and consider the submodule \(M\) of \(R^2\) generated by the elements
\((x^2-1,x-1)\) and \((x^2+x,x)\). 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 Polynomial Rings and Ring Homomorphism Kernels