2. Let R be a commutative ring with identity and let u be a unit in...

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2. Let R be a commutative ring with identity and let u be a unit in R. Show that if a bu, then (a) = (b). = 3. For the following ideals I in the rings R, describe the quotient ring R/I by finding the distinct elements in R/I. (a) R = Zx Z and I = {(0, k) | ke Z} (b) R = Zx Z and I = {(0, 2k) | ke Z}. (c) R = Zx Z₂ and I = {(k, 0) | ke Z}. (d) R = Zx Z₂ and I = {(0, k) | k € Z₂}. 2. Let R be a commutative ring with identity and let u be a unit in R. Show that if a bu, then (a) = (b). = 3. For the following ideals I in the rings R, describe the quotient ring R/I by finding the distinct elements in R/I. (a) R = Zx Z and I = {(0, k) | ke Z} (b) R = Zx Z and I = {(0, 2k) | ke Z}. (c) R = Zx Z₂ and I = {(k, 0) | ke Z}. (d) R = Zx Z₂ and I = {(0, k) | k € Z₂}. 2. Let R be a commutative ring with identity and let u be a unit in R. Show that if a bu, then (a) = (b). = 3. For the following ideals I in the rings R, describe the quotient ring R/I by finding the distinct elements in R/I. (a) R = Zx Z and I = {(0, k) | ke Z} (b) R = Zx Z and I = {(0, 2k) | ke Z}. (c) R = Zx Z₂ and I = {(k, 0) | ke Z}. (d) R = Zx Z₂ and I = {(0, k) | k € Z₂}.

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2 Let R be a commutative ring with identity and u be a unit in R We want to show that if a bu then t... View the full answer