Ideals and Factor Rings - Problem:
Note: | | is trying to denote a matrix
If R =
|S S|
|0 S|
and A =
|0 S|
|0 0|
, S and ring, show that A is an ideal of R and describe the cosets in R/A
Rings - Please see the attached file for the fully formatted problems.
Describe the rings: Z[x]/(x2 - 3, 2x + 4), Z[i]/(2 + i)
Describe the Rings - Please see the attached file for the fully formatted problem.
Describe the rings:
Z[x]/(x2-3, 2x+4),Z[i]/(2+i)
Rings that are not Isomorphic - I need to prove that the rings 2Z and 3Z are not isomorphic. I must also be able to show that the rings R (set of reals) and C (set of complex) are not isomorphic.
Commutative Rings, Homomorphisms and Ideals - Show that if R and S are commutative rings with 1, phi:R-->S is a homomorphism of R onto S, and I is an ideal of R, then phi[I]={phi(r): r included in I} is an ideal of S.