Question

In: Advanced Math

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

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

Solutions

Expert Solution


Related Solutions

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...
let r1 and r2 be the relations represented as r1 (ABC) and r2 (ADE) .Assume the corresponding domains of both the tables are same.r1 has 2000 tuples and r2 has 4500 tuples 1.common tuples between r1 and r2 are 500, what would be the resultant number of tuples for r1-r2, justify your answer 2.assuming 500 as the common tuples between r1 and r2,what is the maximum number of tuples that results in ]] A( r1) U ]] A r2. justify...
A. Consider two concentric spherical structures of radius r1 and r2 such that r1 < r2...
A. Consider two concentric spherical structures of radius r1 and r2 such that r1 < r2 and full load Q and -2Q respectively. Calculate the magnitude of the field on ́ectrico in all three regions, i.e. within the smaller sphere, between the spheres and outside the sphere of the larger radius. Where does the electric field point to for this system? (no matter what material these concentric spherical are made of) B. Two cylindrical coaxial shells with radius r1 and...
A field is a commutative ring with unity in which every nonzero element is a unit....
A field is a commutative ring with unity in which every nonzero element is a unit. Question: Show that Z_5 under addition and multiplication mod 5 is a field. (state the operations, identities, inverses)
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)?
Two hoops have the same mass M. Their radii are R1 and R2 = 2 R1....
Two hoops have the same mass M. Their radii are R1 and R2 = 2 R1. Similarly, two uniform disks also have mass M and the radii, R1 and R2. Which of these objects has the largest moment of inertia about the axis perpendicular to the screen and through the center of the hoop or disk? The moment of inertia of a uniform disk of mass mand radius r about its center is (1/2)mr2; for a hoop it is mr2....
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.
let S in Rn be convex set. show that u point in S is extreme point...
let S in Rn be convex set. show that u point in S is extreme point of S if and only if u is not convex combination of other points of S.
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT