But when we include 12, we also have to include all possible sums and products in order to ensure that we still have a ring; the operations of addition and multiplication need to be close...But when we include 12, we also have to include all possible sums and products in order to ensure that we still have a ring; the operations of addition and multiplication need to be closed, of course. El campo de fracciones de un dominio integralD is D′/I, with D′ and I as defined above.