Is the ring Z/6Z and Z6 are isomorphic.

Show, by example, that for fixed nonzero elements a and b in a ring, the equation ax = b can have more than one solution.  HOw does this compare with groups?

Let m and n be positive integers. Show that the quotient ring if m and n are coprime. nZ nmZ has a multiplicative identity if and only

Let P be a prime ideal and R a commutative ring with identity. If R/P is an integral domain, explain why R/P cannot be the ring with one element. Also explain why P is not equal to R in this scenario.