Suppose that Φ: R --> S is a ring homomorphism and that the imageof Φ is not {0}. If R has a unity and S is an integral domain, showthat Φ carries the unity of R to the unity of S. Give an example toshow that the preceding statement need not be true if S is not anintegral domain.

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Q: If in a ring R every x E R satisfies x2 = x, Prove that R must be commutative.

A: Answer and explanation is given below...

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

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Q: Let (R,+, ⋅) be a ring with additive identity 0. Prove that for all x∈R, 0⋅x=0 and ? ⋅ 0 = 0.

A: Solution

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Q: The ring Zs[i] has no proper ideals True False O O

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Q: 1. Suppose that p: R → S is a ring homomorphism and that the image of o is not {0}. If R has a unity…

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A: That's easy. Thumb up. Have a great day!!!

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