Show that the set 4Z U 5Z is not a subring of the integer ring Z:

Q: Is there a ring homomorphism from the reals to some ring whosekernel is the integers?

A: To Do: We have to check whether there is a ring homomorphism from the reals to some ring whose…

Q: Let G=Z5xZ6X Z9 X Z12- Find the elementary divisors and invariant factors of G.

A: Solution :-

Q: 5. A division ring is a ring with identity in which every nonzero element has a multi- plicative…

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Q: Show that the set Q(√2) = {a+b√2, a, b € Q} is a ring, under operations of multiplication and…

A: The set Q2=a+b2 , a , b∈Q  and operations under multiplication and addition define by :…

Q: Show that A is ideal of A+B? IS an

A: According to questionWe have to show that A is an ideal of A+B

Q: Find two examples of a ring in which {0R} is maximal.

A: Answer

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

A: Answer 1: Must know:The cancellation laws hold in a ring R if an only if R has no zero divisors

Q: Show that the intersection of any collection of subrings of a ring R is also a subring.

A: Sol:- To show that the intersection of any collection of subrings of a ring R is also a subring, we…

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: finite commutative ring with more than one element ar સા

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Q: The zero ring ⟨{0}, #, ∗⟩ is a field with respect to addition # and multiplication ∗ because it…

A: The given Statement is  the Zero ring is a field .

Q: [.gl g(x,y) de L L is curve arc y = 1 x², from (0,0) to (1,0.5) and g(x,y)=x 2

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Q: Show that Ø is a ring homomorphism.

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Q: Let R be a commutative ring with unity. Suppose that the only idealsof R are {0} and R. Show that R…

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Q: Define the binary operations + and . On Z by a +b = a+b-1 and a.b= a+b- ab for all ab belongs to Z.…

A: We will use basic properties of ring homomorphism and integral domain.

Q: Let R be a ring with unity and assume p, q, r ∈ R∗ Find (pqr)-1and also prove that it’s the inverse…

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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: 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: 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: The triple ⟨911Z, +, ⋅⟩ forms a commutative ring. It is also an integral domain. However, it is not…

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Q: Let (R, +, .) be a nontrivial ring with * identity, prove that 1 0

A: It is given that (R,+, .) be a nontrivial ring with identity. Now we have to show that 1≠0. So, (R,…

Q: Show that in a ring R cancellation laws hold if and only if R has no zero divisors.

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

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Q: Show that a commutative ring R with unity is a field if and only if its only two ideals are (0) and…

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