Answer to Question #47329 in Abstract Algebra for ayush kumar

Question

1 a) Prove or disprove that we can define a multiplication on R3 = {a+ bi + cj|a,b,c belong to R} such that
i= - 1= j2 .
b) Use the Euclidean algorithm to find a g.c.d. of x5+ x+ 1 and x4+x3+x+1 in Z2[x].

c) If f :R tends to S is a ring homomorphism, then show that char R greater than equal to char S.