However, a non-Noetherian ring can be a subring of a Noetherian ring. Since any integral domain is a subring of a field, any integral domain that is not Noetherian provides an example. To give a less trivial example, The ring of rational functions generated by x and y&hairsp;/xn over a field k is a subring of the field k(x,y) in only two variables.
however a non-noetherian ring can be a subring of a noetherian ring since any integral domain is a subring of a field any integral domain that is not noetherian provides an example to give a less trivial example the ring of rational functions generated by x and y&hairsp;/xn over a field k is a subring of the field k(xy) in only two variables