Question

Let R be a ring and let M and N be right R-modules. Assume that the...

Let R be a ring and let M and N be right R-modules. Assume that the only R-homorphisms M → N and N → M are 0 maps. Prove that EndR(M⊕N) ∼= EndR(M) ⊕ EndR(N) (direct sum of rings). Remember the convention used for composition of R-homomorphismps.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let R be a ring, and assume that r^2 = r for all r ∈ R....
Let R be a ring, and assume that r^2 = r for all r ∈ R. (a) Prove that r + r = 0 for all r ∈ R. (b) Prove that R is commutative.
Let R be a ring, and let N be an ideal of R. Let γ :...
Let R be a ring, and let N be an ideal of R. Let γ : R → R/N be the canonical homomorphism. (a) Let I be an ideal of R such that I ⊇ N. Prove that γ−1[γ[I]] = I. (b) Prove that mapping {ideals I of R such that I ⊇ N} −→ {ideals of R/N} is a well-defined bijection between two sets
Let R be a ring. For n ≥ 0, let In = {a ∈ R |...
Let R be a ring. For n ≥ 0, let In = {a ∈ R | 5na = 0}. Show that I = ⋃ In is an ideal of R. Please use the strategies from Chapter 14 in Joseph Gallian's "Contemporary Abstract Algebra."
Let R be a ring. For n ≥ 0, let In = {a ∈ R |...
Let R be a ring. For n ≥ 0, let In = {a ∈ R | 5na = 0}. Show that I = ⋃ In is an ideal of R. Please use the strategies from Chapter 14 in Joseph Gallian's "Contemporary Abstract Algebra."
Let R be a ring. For n > or equal to 0, let In = {a...
Let R be a ring. For n > or equal to 0, let In = {a element of R | 5na = 0}. Show that I = union of In is an ideal of R.
Prove that a ring R is a division ring if and only if it's only left-ideals...
Prove that a ring R is a division ring if and only if it's only left-ideals and right-ideals are {0} and R. Please answer in a way to explain as most of these words are unfamiliar.
Let I, M be ideals of the commutative ring R. Show that M is a maximal...
Let I, M be ideals of the commutative ring R. Show that M is a maximal ideal of R if and only if M/I is a maximal ideal of R/I.
(a) A circular ring has radius r and mass M. Let L be the axis of...
(a) A circular ring has radius r and mass M. Let L be the axis of the ring (the line that is perpendicular to the plane of the ring and that passes through the center of the ring). What is the force on a mass m that is located on L, at a distance x from the center of the ring? (b) A hole with radius R is cut out from an innite at sheet with mass density (kg=m2). What...
Let R be a ring, and set I:={(r,0)|r∈R}. Prove that I is an ideal of R×R,...
Let R be a ring, and set I:={(r,0)|r∈R}. Prove that I is an ideal of R×R, and that (R×R)/I is isomorphism to R.
Prove that if every short exact sequence of modules 0-> Q -> M -> N ->...
Prove that if every short exact sequence of modules 0-> Q -> M -> N -> 0 splits then Q is a projective module.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT