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.
Commutative rings, homomorphisms and ideals are investigated.
Ideals and rings - See attached
Let n=md, with m and d being positive integers. Show that the principal ideal generated by [m] in Z_n has exactly d elements....
Ideals and Rings : Homomorphisms - Problem:
Prove the Second Isomorphism Theorem: If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S, respectively, and (S+A)/A isom ...
Commutative Rings, Prime Ideals and Maximal Ideals - 1.-Give a example of a commutative ring that has a maximal ideal that is not a prime ideal.
2.- Prove that I=<2+2i> is not a prime ideal of Z[i] . How many elements are in Z[i]/I ? What is the char ...
Rings, Fields and Maximal Ideals - If R is a commutative ring with unit element and M is an ideal of R then M is a maximal ideal of R if and only if R/M is a field