Recent content by Rfields

P is fixed. I know that Z/pZ is a field, for a given prime p. Is that what you mean? To show that ZxZ /Zx{0} is isomorphic to Z, I'd need to create a bijective function from ZxZ / Zx{0} where f(a + b) = f(a) + f(b) and f(ab)= f(a)*f(b). Are you hinting that since p is a prime integer, Z/M...

Homework Statement M = {(pa,b) | a, b are integers and p is prime} Prove that M is a maximal ideal in Z x Z Homework Equations The Attempt at a Solution I know that there are two ways to prove an ideal is maximal: You can show that, in the ring R, whenever J is an ideal such...

Homework Statement Let I and J be ideals in R. Is the set K = {ab|a is an element of I, b is an element of J} an ideal in R? Homework Equations Conditions for an ideal, I of a ring R; (i)I is nonempty, (ii)for any c,e ε I: c-eεI (iii)for any c ε I, rεR: rc, cr ε I. The Attempt at a Solution...