## Rocky Mountain Journal of Mathematics

### Sets of lengths of powers of a variable

#### 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 $\mathfrak{m} ^2=0$.

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 729-741.

Dates
First available in Project Euclid: 23 July 2019

https://projecteuclid.org/euclid.rmjm/1563847230

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-729

Mathematical Reviews number (MathSciNet)
MR3983297

Zentralblatt MATH identifier
07088333

#### Citation

Belshoff, Richard; Kline, Daniel; Rogers, Mark W. Sets of lengths of powers of a variable. Rocky Mountain J. Math. 49 (2019), no. 3, 729--741. doi:10.1216/RMJ-2019-49-3-729. https://projecteuclid.org/euclid.rmjm/1563847230

#### References

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