Abstract
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 $(R, \mathfrak{m} )$ is an Artinian local ring with $\mathfrak{m} ^2=0$.
Citation
Richard Belshoff. Daniel Kline. Mark W. Rogers. "Sets of lengths of powers of a variable." Rocky Mountain J. Math. 49 (3) 729 - 741, 2019. https://doi.org/10.1216/RMJ-2019-49-3-729
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