subject: abstract algebra

Please show all work and justify each step!

Each part describes an algebraic object. For each description, either give a concrete example of such an object, or, say why an example cannot exist. In case you give an example, I do not require you to prove that it has the properties but the example must be concretely defined. In case you say that such an example cannot exist, give a short (!) justification/proof. (a) A finite non-commutative ring with identity (b) A field with 6 elements. (c) Three rings with 12 elements such that any two of these rings are not isomorphic. (d) For a ring R: an ideal I of the product ring R x R so that (RX R) / I is isomorphic to R