KLAŠKA, Jiří a Ladislav SKULA. Law of inertia for the factorization of cubic polynomials - the imaginary case. Utilitas Mathematica. Winnipeg, Kanada: Util Math Publ Inc, 2017, roč. 103, June, s. 99-109. ISSN 0315-3681. |
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@article{1382602, author = {Klaška, Jiří and Skula, Ladislav}, article_location = {Winnipeg, Kanada}, article_number = {June}, keywords = {cubic polynomial; type of factorization; discriminant}, language = {eng}, issn = {0315-3681}, journal = {Utilitas Mathematica}, title = {Law of inertia for the factorization of cubic polynomials - the imaginary case}, url = {http://91.203.202.198/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml}, volume = {103}, year = {2017} }
TY - JOUR ID - 1382602 AU - Klaška, Jiří - Skula, Ladislav PY - 2017 TI - Law of inertia for the factorization of cubic polynomials - the imaginary case JF - Utilitas Mathematica VL - 103 IS - June SP - 99-109 EP - 99-109 PB - Util Math Publ Inc SN - 03153681 KW - cubic polynomial KW - type of factorization KW - discriminant UR - http://91.203.202.198/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml L2 - http://91.203.202.198/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml N2 - Let D be a square-free positive integer not divisible by 3 such that the class number h(-3D) of Q((-3D)^(1/2)) is also not divisible by 3. We prove that all cubic polynomials f (x) = x^3 + ax^2 + bx + c in Z[x] with a discriminant D have the same type of factorization over any Galois field F_p, where p is a prime bigger than 3. Moreover, we show that any polynomial f(x) with such a discriminant D has a rational integer root. A complete discussion of the case D = 0 is also included. ER -
KLAŠKA, Jiří a Ladislav SKULA. Law of inertia for the factorization of cubic polynomials - the imaginary case. \textit{Utilitas Mathematica}. Winnipeg, Kanada: Util Math Publ Inc, 2017, roč.~103, June, s.~99-109. ISSN~0315-3681.
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