The key to this particular problem is making sure all of the elements are of the form a + b5 Let (a + b5) & (c+ d5) € A Consider bd(¥5)² (a + b5) · (c+ dW5) = ac + ad5 + bcỷ5+i Note bd(5) ¢ A. This is not closed over multipliciation and therefore not a ring. Can you explain why bd(5) £ A?

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: 18. Prove that in a Euclidean ring R, (a, b) can be found as follows : b= 90 a+ r,, where d (r) <d…

A:

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A: Please check the answer in next step

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Q: 37. Explain why in any ring R and any r, y, z E R: (a) 0+z =0 (b) 1 =I (c) 0+1=1. (d) z(y+ 2) = ry+…

A: We are given with several multiple subparts kindly repost the other as next question

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