say R1, R2,...., Rn are commutative rings with unity. Show that U(R1 + R2 +.... +...

say R₁, R₂,...., R_n are commutative rings with unity. Show that U(R₁ + R₂ +.... + R_n) = U( R₁) + U(R₂)+ .... U(R_n). Where U - is the units of the ring.

Expert Solution

Colby Messinger answered 2 years ago

Let R and S be commutative rings with unity. (a) Let I be an ideal of...

Let R and S be commutative rings with unity. (a) Let I be an ideal of R and let J be an ideal of S. Prove that I × J = {(a, b) | a ∈ I, b ∈ J} is an ideal of R × S. (b) (Harder!) Let L be any ideal of R × S. Prove that there exists an ideal I of R and an ideal J of S such that L = I × J.

let r1 and r2 be the relations represented as r1 (ABC) and r2 (ADE) .Assume the...

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A. Consider two concentric spherical structures of radius r1 and r2 such that r1 < r2...

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Let R be a commutative ring with unity. If I is a prime ideal of R,...

Let R be a commutative ring with unity. If I is a prime ideal of R, prove that I[x] is a prime ideal of R[x].

Suppose R1,R2,...,Rn are mutually independent and uniformly distributed random variables on [0,1]. Assume R(1) ≤ R(2)...

Suppose R1,R2,...,Rn are mutually independent and uniformly distributed random variables on [0,1]. Assume R(1) ≤ R(2) ≤···≤ R(n) are the order statistics of the R1,R2,...,Rn. It is given that 1 ≤ a < b ≤ n. What is the distribution of R(b)−R(a)?

Let R be a commutative ring with unity. Prove that f(x) is R[x] is a unit...

Let R be a commutative ring with unity. Prove that f(x) is R[x] is a unit in R[x] iff f(x)=a is of degree 0 and is a unit in R.

Two hoops have the same mass M. Their radii are R1 and R2 = 2 R1....

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let S in Rn be convex set. show that u point in S is extreme point...

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Consider the following relations: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater...

Consider the following relations: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than or equal to relation R3 = {(a, b) ∈ R2 ∣ a < b}, the less than relation R4 = {(a, b) ∈ R2 ∣ a ≤ b}, the less than or equal to relation R5 = {(a, b) ∈ R2 ∣ a = b}, the equal to relation...

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