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 xn in R[x], where (R;m) is an Artinian local ring with m2 = 0.
Artinian local ring, nonunique factorization, polynomial.
Belshoff, Richard, Daniel Kline, and Mark W. Rogers. "Sets of lengths of powers of a variable." Rocky Mountain Journal of Mathematics 49, no. 3 (2019): 729-741.
Rocky Mountain Journal of Mathematics