Abstract
Let R be a commutative artinian ring, and f(x) ∈ R[x] be a nonconstant monic polynomial. The main purpose of this paper is to determine the socle series of R[x]/❬f(x)❭ in terms of the socle series of R. As an application of the results proved, it is proved that R is a QF-ring if and only if R[x]/❬f(x)❭ is a QF-ring. As another application, a necessary and sufficient condition for a local artinian ring R having a semisimple ideal B, with R/B a PIR, to be a split extension of a PIR by a semisimple module, is given.