Rocky Mountain Journal of Mathematics

Sets of lengths of powers of a variable

Richard Belshoff, Daniel Kline, and Mark W. Rogers

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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

Permanent link to this document
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

Subjects
Primary: 13A05: Divisibility; factorizations [See also 13F15]
Secondary: 13E10: Artinian rings and modules, finite-dimensional algebras

Keywords
nonunique factorization Artinian local ring polynomial

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


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References

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