Let S = {4, 7, 41, 74}. Recall that the power set P (S) of S is the set of all subsets of the set S. Notice that (P (S);A,n) is a commutative ring with unity, where AAB = (A – B)U (B – A) for any A, BE P (S) and -,U,n are the usual set difference, union, and intersection, respectively. List the elements of the following sets: a. The additive identity, which is the element with respect to A, is the set b. The the additive inverse of A = {4}, which is the inverse of A with respect to A, is the set c. The unity is the set

Q: Q6: Define the Boolean ring. Is (Z,+,.) Boolean?

A: .

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Q: The characteristics of local rings is either 0 or prime.

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Q: Let 2 = {a, b, c}. Write down all possible o-algebras on N.

A: Given: Ω=a,b,c

Q: a. Complete the below chart of ring ( image 2 ), providing the values for a, b, c, d ,e f, g, h, i,…

A: Given: Addition and multiplication table of ℤ8. To find: a. Values of a, b, c, d ,e, f, g, h, i, j…

Q: Define commutative ring.

A: Answer:

Q: by example thai it is an sible to find ideals A,B,C R Such that a

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Q: The number of zero divisors in the ring Z80

A: Step:-1 Theorem:- If  gcda, n>1  and n- a then [a] is a zero divisor in ℤn. Also, we know ϕn =…

Q: Let CR,t,,) be a Commutative ring ?

A: First I recall you Definition of commutative ring.  A commutative ring is ring in which…

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Q: Q29: Define the Boolean ring. Is (Z,+,.) Boolean?

A:

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Q: Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a…

A: We have to solve given problem:

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Q: Give an example of a noncommutative ring with unity.

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Q: Prove that every Boolean ring is commutative. Is the converse true? Explain your answer.

A: We can solve this using definition of boolean ring

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Q: Q: Define the concept of the ring. Is (Z+.) a ring? What's about (Z, +,.)?

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Q: Demonstrate or explain why the system (P(R#), +, *) is a ring with identity and is a commutative…

A: (i) Let,           f(x) = anxn + an-1xn-1 + . . . . . . . . + a1x + a0   ∈ P(R#)        Then,…

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Q: he ring 3z is isomorphic to the ring 5Z O False O True K

A: