53 020
Assignments Done
97,8%
Successfully Done
In October 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Abstract Algebra Question for Melvin Henriksen

Question #16815
Let R be a ring with center C. Show that a right ideal A of R is an ideal if:
the factor group R/A is cyclic, or isomorphic to a subgroup of Q.
Expert's answer
Since S ⊇ C, End(S(R/A)) is a subring of End(C(R/A)). Therefore, we have End(C(R/A)) is a commutative ring. Next, suppose " R/A is a cyclic left C-module " holds. Then C(R/A) can be identified with C/I for some ideal I of C. Then End(C(R/A)) ∼ End(C(C/I)) ∼ End(C/I (C/I)) ∼ C/I is a commutative ring, so we have End(C(R/A)) is a commutative ring. Finally, under " The factor group R/A is cyclic, or isomorphic to a subgroup of Q ", any Z-endomorphism of R/A is induced by multiplication by an integer or a rational number. Since End(S(R/A)) is a subring of End(Z(R/A)), we have that factor group R/A is cyclic, or isomorphic to a subgroup of Q

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question