Q) Let (H,+10, -10) be a subring of the ring (Z10, +10. -10 ), where H = {[0], [2], [4], [6], [8]}. Then answer the following: 1) Fill this table •10 [0] [2] [4] [6] | [8] [0] [2] [4] [6] [8] 2) Find all the idempotent elements of H. 3) Find all the nilpotent elements of H. 1 of 1

Q: 5) If you know the roots for a polynomial are x = -3, 1, and 2   which of the following could be the…

A: Given: If you know the roots for a polynomial are x = -3, 1, and 2 which of the following could be…

Q: Q1. a) Give an example of a semi-ring that is not a semi -algebra. b) Give an example of a…

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Q: Construct the multiplication table for the ring Z/6Z.

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Q: 12. Let R² be the set of all pairs of real numbers R² = {(a,b)|a, b = R}. The addition is still…

A: is the set of all pairs of real numbers The multiplication is defined by

Q: How many distinct cosets are there in the factor ring Z[i] / ? Explain your answer.

A: Given: Let's determine the number of distinct cosets of the factor ring ℤi3+i.

Q: Enter the multiplicative inverse of the element [10] x + [13] in the ring z-[x]

A: We need to fin the multiplicative inverse of the element [10]20x+[13]20 in the ring Z20x. Let…

Q: Explain why the ring of integers Z under usual addition and multiplication is not a field.

A: Given that the set of integers Z is a ring under addition and multiplication. We know that an…

Q: Q2: (A) Choose the correct answer for each of the following: 1. The cancellation law holds in a. any…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Explain why 3Z is not an ideal in Q

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Q: Suppose that R₁ is a ring with addition +1 and multiplication 1, and that R2 is a ring with addition…

A: Answer in steps:We need to show that (R₁ × R₂, +, ·) satisfies all the axioms for a ring.i.Closure…