A note on the socle of certain types of f-rings

Document Type : Research Paper


University of South Africa


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 consist entirely of bounded elements. It
is not too stringent, and is satisfied, for instance, by rings of
continuous functions.