Lot R by unity. a commutative ring with (01) Prove that if gER, then a R={arIVER} 1) an ає idral of R₁ (6) is aR a maximal ideal. 85

Q: (15 points) Prove the ring Z[√−2] = {a+b√−2 | a,b ≤ Z} is a Euclidean domain with norm 8(a+b√2) = a²…

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A: First Suppose that, ϕ: R → R' be ring homomorphism ϕ(a-b)= ϕ(a)-ϕ(b)

Q: Let M2(Z) be a ring and =(( ), a,b e Z}. Then S is ideal %D .of M2(Z) l choose one true Error

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Q: It is known that (ℤ,⋆,⊙) where ? ⋆ ? = ? + ? − 1 and ? ⊙ ? = ? + ? − ?? is a ring. Does it have…

A: Please check step 2 for the solution.

Q: If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+(AnC) = (A B) + (AnC).

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Q: 8. If 1 and 2 are two ideals of the ring R, prove that the set 1₁+= {x+yx Eh, yЄh} is an ideal of R…

A: To prove that the set I1​+I2​={x+y∣x∈I1​,y∈I2​}  is an ideal of the ring (R) and contains each of…

Q: if the following ideals are Maximal, Prime but Prime. You do not have to provide reasons i. (the…

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Q: 2. In the ring (4Z, +,.), the ideal (8) is (a) not prime (b) maximal (c) maximal and not prime (d)…

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Q: 1. Let ./ be an ideal of the ring R. Show that the ring R/J is commutative if and only if xy-yx J…

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Q: a ring and až a for prove that R is. Let R be all aER Then commutative (6) Let A and B. commutati ve…

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