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...