For an integral extension from A to B, every one of these objects in B “lies over” another in A by one of the Cohen-Seidenberg theorems. The intersection of all of these objects is the set of nilpotent elements, (15[1])called the nilradical. (15[2])These objects correspond to irreducible subvarieties by the (-5[1])Nullstellensatz. The Zariski topology (15[1]-5[1])is defined on the set of these objects, which is the spectrum of a (*) ring. (-5[1])A set S (10[1])is one of these subsets if and only if the quotient R over S is an integral domain. If an element xy is in one of these subsets, (10[1])then exactly one of x or y is an element as well in a generalization of Euclid’s lemma. In a Dedekind ring, every proper ideal has a unique factorization into these ideals. (10[1])For 10 points, name these ideals that, in the ring of integers, include the multiples of two, three, five, and seven. (10[1])■END■ (0[1])