Back to Search
Start Over
On Least Common Multiples of Polynomials in Z / n Z [ x ].
- Source :
- Communications in Algebra; Jun2012, Vol. 40 Issue 6, p2066-2080, 15p
- Publication Year :
- 2012
-
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]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 40
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 76607010
- Full Text :
- https://doi.org/10.1080/00927872.2011.571732