Let Z∗ be the set of integers together with ⊕ and ⊗ defined by a ⊕ b = a + b − 1 a ⊗ b = ab − a − b + 2. Show that Z∗ is a ring by finding an isomorphism from Z to Z∗. (Hint: What is the multiplicative identity in Z∗?)

Q: D. Given the set F= {0, a, b, c, d} with operations + and * and the following tables, assume that…

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Q: 6. If a and b are not zero divisors in a ring R, prove that ab is not a zero divisor.

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Q: 3. Consider the set {a+b√2: a, b E Z} with the usual addition and multiplication. Show that this is…

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Q: A ring may have more than one identity element for multiplication? T or F

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

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Q: Determine if the set {x + y∛2 : x,y ∈ Z} is a ring. If so, please prove why. (Z represents integers)

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Q: Define a new addition ⊕ and multiplication ⊙ on ℚ by               a ⊕ b = a + b + 1 and a ⊙ b = ab…

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Q: et R be a ring and assume a∈R is not a zero divisor. If ab=ac for some b,c∈R, then b=c

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Q: 4. Let a 0 in the ring of integers Z. Find b = Z such that ab but (a) = (b).

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