a. Complete the below chart of ring ( image 2 ), providing the values for a, b, c, d ,e f, g, h, i, j ,k , l , m ,n, p, r. b. Then determine whether the ( image 2) is a field or not. c. Explain why

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Q: be a field and let c,d e F. Show that c · (-d) = -(c d).

A: Associative Property of Field F for a,b,c∈F a·b·c=a·b·c

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

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A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

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A: We have to solve given problem:

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A: Associative Property of Field F for a,b,c∈F a·b·c=a·b·c

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Q: Given a set Q× Q under operations: (21, Y1) + (#2, Y2) = (¤1 + #2, Y1 + y2), (21,41) (22, Y2) =…

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Q: If R is a U.F.D., then R[x, y] is a U.F.D. If F is a field, then F [x, y] is à U.F.D.

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Q: handwritten solution asap for part b

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Let F be a field and let a, b e F. Show that (-a) - b= -(a - b).

A: Introduction: Associative property of field F for a,b,c∈F. (a·b)·c=a·(b·c)

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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

Q: Given a set Q x Q under operations: (¤1, Y1) + (x2, Y2) = (x1 + x2, Y1 + y2), (*1, Y1) · (*2, Y2) =…

A: The given question is related to Abstract Algebra. The solution is explained below.