Sets of Lengths of Powers of a Variable
  A positive integer k is a length of a polynomial if that polynomial factors into a product of k irreducible polynomials. We find the set of lengths of polynomials of the form x^n in R[x], where (R, m) is an Artinian local ring with m^2 = 0. 
Richard Belshoff, Daniel Kline, Mark W. Rogers
math.AC