TY - JOUR
T1 - A Generalization of a Lemma of Sullivan
AU - Luca, Florian
AU - Rzedowski-Calderón, Martha
AU - Maldonado-Ramírez, Myriam Rosalía
PY - 2012/7
Y1 - 2012/7
N2 - Consider an irreducible polynomial of the form f(X) = X p - aX - b ∈ F[X] and α a root of f(X), where F is a field of characteristic p. In 1975, F.J. Sullivan stated a lemma that provides the trace, taken with respect to the extension F(α)/F, of elements of the form α n, where 0 ≤ n ≤ p 2 - 1. We present a generalization of Sullivan's Lemma and provide another proof of the original lemma. We explain how computing Tr(α n) for n & p r can be reduced to computing the traces Tr(α m) for all m ≤ r(p - 1).
AB - Consider an irreducible polynomial of the form f(X) = X p - aX - b ∈ F[X] and α a root of f(X), where F is a field of characteristic p. In 1975, F.J. Sullivan stated a lemma that provides the trace, taken with respect to the extension F(α)/F, of elements of the form α n, where 0 ≤ n ≤ p 2 - 1. We present a generalization of Sullivan's Lemma and provide another proof of the original lemma. We explain how computing Tr(α n) for n & p r can be reduced to computing the traces Tr(α m) for all m ≤ r(p - 1).
KW - Trace
KW - Trinomials
UR - http://www.scopus.com/inward/record.url?scp=84863821875&partnerID=8YFLogxK
U2 - 10.1080/00927872.2011.561391
DO - 10.1080/00927872.2011.561391
M3 - Artículo
SN - 0092-7872
VL - 40
SP - 2301
EP - 2308
JO - Communications in Algebra
JF - Communications in Algebra
IS - 7
ER -