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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2010 • Question 4

Question

Math 6310 • Algebra Fall 2010 • Question 4

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

Raw LaTeX

Set \(R=\mathbb{Q}[x]\), and consider the submodule \(M\) of \(R^2\) generated by the elements
\((1-2x,-x^2)\) and \((1-x,x-x^2)\). Express \(R^2/M\) 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