Yıl 2017, Cilt 22, Sayı 22, Sayfalar 170 - 186 2017-07-11

Polynomials Inducing the Zero Function on Local Rings

Mark W. Rogers [1] , Cameron Wickham [2]

143 124

For a Noetherian local ring $(R, \f{m})$ having a finite residue field of
  cardinality $q$, we study the connections between the ideal \zf{R} of $R[x]$,
  which is the set of polynomials that vanish on $R$, and the ideal \zf{\f{m}},
  the polynomials that vanish on \f{m}, using polynomials of the form
  $\pi(x) = \prod_{i = 1}^{q} (x - c_{i})$, where $c_{1}, \ldots, c_{q}$ is a
  set of representatives of the residue classes of \f{m}.  In particular, when
  $R$ is Henselian we show that a generating set for \zf{R} may be obtained from
  a generating set for \zf{\f{m}} by composing with $\pi(x)$.

Finite ring, polynomial function
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Konular Matematik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Mark W. Rogers

Yazar: Cameron Wickham

Bibtex @araştırma makalesi { ieja325942, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {22}, pages = {170 - 186}, doi = {10.24330/ieja.325942}, title = {Polynomials Inducing the Zero Function on Local Rings}, key = {cite}, author = {Rogers, Mark W. and Wickham, Cameron} }
APA Rogers, M , Wickham, C . (2017). Polynomials Inducing the Zero Function on Local Rings. International Electronic Journal of Algebra, 22 (22), 170-186. DOI: 10.24330/ieja.325942
MLA Rogers, M , Wickham, C . "Polynomials Inducing the Zero Function on Local Rings". International Electronic Journal of Algebra 22 (2017): 170-186 <http://dergipark.gov.tr/ieja/issue/30344/325942>
Chicago Rogers, M , Wickham, C . "Polynomials Inducing the Zero Function on Local Rings". International Electronic Journal of Algebra 22 (2017): 170-186
RIS TY - JOUR T1 - Polynomials Inducing the Zero Function on Local Rings AU - Mark W. Rogers , Cameron Wickham Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.325942 DO - 10.24330/ieja.325942 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 170 EP - 186 VL - 22 IS - 22 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.325942 UR - http://dx.doi.org/10.24330/ieja.325942 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra Polynomials Inducing the Zero Function on Local Rings %A Mark W. Rogers , Cameron Wickham %T Polynomials Inducing the Zero Function on Local Rings %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 22 %N 22 %R doi: 10.24330/ieja.325942 %U 10.24330/ieja.325942
ISNAD Rogers, Mark W. , Wickham, Cameron . "Polynomials Inducing the Zero Function on Local Rings". International Electronic Journal of Algebra 22 / 22 (Temmuz 2017): 170-186. http://dx.doi.org/10.24330/ieja.325942