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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 2

Question

Math 6310 • Algebra Fall 2007 • Question 2

Let \(I\subseteq \mathbb {Z}[x]\) be an ideal consisting of all polynomials \(a_0+a_1x+a_2x^2+\cdots \) such that 8 divides \(a_0\), 4 divides \(a_1\) and 2 divides all other coefficients. Find a finite set of generators of the ideal \(I\).

Raw LaTeX

Let \(I\subseteq \mathbb{Z}[x]\) be an ideal consisting of all polynomials
\(a_0+a_1x+a_2x^2+\cdots\) such that 8 divides \(a_0\), 4 divides \(a_1\) and 2 divides all
other coefficients. Find a finite set of generators of the ideal \(I\).

Topic Tags

Galois Groups of Polynomials Ideals and Quotient Rings Polynomial Rings and Prime Ideals Polynomial Rings and Ring Homomorphism Kernels