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#1 2010-05-18 17:24:00

GOKILL
Member
Registered: 2010-03-19
Posts: 26

Abstract Algebra, COOL 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 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!

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#2 2010-07-01 21:25:31

jk22
Member
Registered: 2010-06-14
Posts: 33

Re: Abstract Algebra, COOL Homework :D

Hi, nice to meet you.

for #1 could we write :

let c=0 :


let a=0 :
, the square of any number is 0

-------

from

:

right-multiply with a :

let a=1,


but since the square of b is 0 :

, which can be written :

Last edited by jk22 (2010-07-01 21:27:44)

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#3 2010-07-02 17:51:12

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Abstract Algebra, COOL Homework :D

Something is wrong with #2, the claimed generator for I isn't even in I.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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