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Survey of Modern Algebr: The system of quaternions. Follow the step to talk about the essay.

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The system of quaternions was discovered by William Rowan Hamilton on the afternoon of Monday, October 16, 1843, as he walked along Royal Canal in Dublin. A quaternion is an abstract symbol of the form a + bi + cj + dk, where a, b, c, d R are real numbers: H = {a + bi + cj + dk : a, b, c, d in R. The “imaginary units” i,j, k are abstract symbols satisfying the following multiplication rules: i^2+j^2+ k^2 = ijk=1. One can check that {H, +, *, 0, 1} is a ring. However, it is not a commutative ring because (for example) we have ij =-k and ji=-k not eaqual k. Your assignment is to write a mathematical paper about the quaternions, including some of exposition and history, but focusing mainly on mathematical results. Here are some ideas:

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