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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2022 • Question 5

Question

Math 6310 • Algebra Fall 2022 • Question 5

Let \(k\) be the field with 2 elements and let \(R=k[x]\). Identify, up to isomorphism, all \(R\)-modules \(M\) with 8 elements (that is \(|M|=8\)) and such that \(M\otimes _R (R/(x^2(x+1)))\) also has 8 elements.

Raw LaTeX

Let \(k\) be the field with 2 elements and let \(R=k[x]\). Identify, up to isomorphism, all \(R\)-modules \(M\) with 8 elements
(that is \(|M|=8\)) and such that \(M\otimes_R (R/(x^2(x+1)))\) also has 8 elements.

Topic Tags

Ideals and Quotient Rings Tensor Products of Modules