Ideal Generated by The Coefficient of a Polynomial Over ℤ_k, k > 1

DOI

10.2991/assehr.k.210508.079How to use a DOI?

Keywords

polynomial ring ℤk, k > 1, Ideal c(f), unit, relative prime

Abstract

Let ℤk, k > 1, k ∈ ℕ be a commutative ring with unity, polynomial f = a0 + a1x + ⋯ + anxn ∈ ℤk[x], ai ∈ ℤk. We can construct c(f) = 〈a0,⋯,an〉 be an ideal of ℤk generated by a0,⋯,an. If (a0,⋯,an) = 1 or ai unit of ℤk for i =0,…,n, then c(f) = ℤk, for k composite. For k is prime, because all of the elements in ℤk is unit, then c(f) = ℤk, for every f ∈ ℤk[x].

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Larasati Onna Roufista
AU  - Indriati Nurul Hidayah
PY  - 2021
DA  - 2021/05/11
TI  - Ideal Generated by The Coefficient of a Polynomial Over ℤk, k > 1
BT  - Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
PB  - Atlantis Press
SP  - 304
EP  - 307
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.210508.079
DO  - 10.2991/assehr.k.210508.079
ID  - Roufista2021
ER  -