1. On Least Common Multiples of Polynomials in Z / n Z [ x ].
- Author
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Werner, NicholasJ.
- Subjects
- *
POLYNOMIALS , *MATRIX rings , *RING theory , *MATHEMATICAL physics , *MATHEMATICAL analysis , *APPROXIMATION theory - Abstract
Let 𝒫(n, D) be the set of all monic polynomials in ℤ/nℤ[x] of degree D. A least common multiple for 𝒫(n, D) is a monic polynomial L ∈ ℤ/nℤ[x] of minimal degree such that f divides L for all f ∈ 𝒫(n, D). A least common multiple for 𝒫(n, D) always exists, but need not be unique; however, its degree is always unique. In this article, we establish some bounds for the degree of a least common multiple for 𝒫(n, D), present constructions for common multiples in ℤ/nℤ[x], and describe a connection to rings of integer-valued polynomials over matrix rings. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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