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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2018 • Question 7

Question

Math 6310 • Algebra Fall 2018 • Question 7

Let \(R=\mathbb {Z}[i]\) be the ring of Gaussian integers. Consider the \(R\)-module \(M\) generated by two elements \(x\) and \(y\), subject to the relations \(ix+2y=0\) and \(2x-iy=0\). How many elements does \(M\) have?

Raw LaTeX

Let \(R=\mathbb{Z}[i]\) be the ring of Gaussian integers. Consider the \(R\)-module \(M\) generated by
two elements \(x\) and \(y\), subject to the relations \(ix+2y=0\) and \(2x-iy=0\). How many elements
does \(M\) have?

Topic Tags

Ideals in Quadratic Integer Rings and Exterior Powers Modules over PIDs