Thread: COOL Abstract Algebra Homework!!! :D

#1
Let R be a ring where .
If (i) R is commutative and (ii) 1+1 and 1+1+1 have inverse in R (1 is unity in R), show that |R|=1.

#2
is the set of all polynomials whose the sum of even degree coefficients is 0 and the sum of odd degree coefficients is 0.
True/False? Explain it!

Thanks for your help

Originally Posted by GOKILL

#1
Let R be a ring where .
If (i) R is commutative and (ii) 1+1 and 1+1+1 have inverse in R (1 is unity in R), show that 1R1=1.

#2
is the set of all polynomials whose the sum of even degree coefficients is 0 and the sum of odd degree coefficients is 0.
True/False? Explain it!

Thanks for your help

both your question have problems!! you should check your question more carefully before submitting it:

in question 1, 1R1 = 1 has no meaning. besides if in you put a = 2 = 1+1 and b = c = 1 you'll get 1 = 0 and so R ={0}!!

in question 2, did you mean ?

I know nothing about Ring Theory but i'd still like to say something here .

Can this help you ?

You should put on clarity the effort you put to posting copies of the same question in two different forums (here) and suffering lack of clarity on both.