A NOTE ON THE SOCLE OF CERTAIN TYPES OF f-RINGS

For any reduced commutative f-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. The condition is that every minimal ideal of the ring consists entirely of bounded elements. This is not too stringent, and is satisfied, for instance, by rings of continuous functions.