 Equivalently, "P" is prime if for any ideals formula_64 we have that formula_65 implies either formula_66 or formula_67 This latter formulation illustrates the idea of ideals as generalizations of elements.A homomorphism from a ring ("R", +, ·) to a ring ("S", ‡, *) is a function "f" from "R" to "S" that preserves the ring operations; namely, such that, for all "a", "b" in "R" the following identities hold