the λ-super socle of the ring of continuous functions

The concept of λ-super socle of c(x), denoted by sλ (x) (that is, the set of elements of c(x) such that the cardinality of their cozerosets are less than λ, where λ is a regular cardinal number with λ ≤ |x|) is introduced and studied. using this concept we extend some of the basic results concerning scf(x), the super socle of c(x) to sλ(x), where λ ≥ℵ0. in particular, we determine spaces x for which scf(x) and sλ(x) coincide. the onepoint λ-compactification of a discrete space is algebraically characterized via the concept of λ-super socle. in fact we show that x is the onepoint λ-compactification of a discrete space y if and only if sλ(x) is a regular ideal and sλ(x)=ox, for some x ϵ x.