Open AccessAkar-akar Polinomial Separable sebagai Pembentuk Perluasan Normal pada Ring Modulo
Author(s) -
Saropah Saropah
Publication year - 2012
Publication title -
cauchy
Language(s) - English
Resource type - Journals
eISSN - 2477-3344
pISSN - 2086-0382
DOI - 10.18860/ca.v2i3.3124
Subject(s) - mathematics , field extension , minimal polynomial (linear algebra) , reciprocal polynomial , irreducible polynomial , matrix polynomial , monic polynomial , field (mathematics) , polynomial , alternating polynomial , square free polynomial , extension (predicate logic) , symmetric polynomial , polynomial ring , separable space , stable polynomial , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , computer science , programming language
One of the most important uses of the ring and field theory is an extension of a broader field so that a polynomial can be found to have roots. In this study researchers took modulo a prima as follows indeterminate coeffcients to search for his roots extension the solutions of that it can seen normal. A field is subject to a polynomial form a set of polynomials , where is a coefficient field its terms modulo a prime number. Of the set of polynomial exists a polynomial is irreducible, it is necessary to extension the field to know the roots of the solution. Suppose to extension of the field is a field . Field is called extension the field over a field , if the field is subfield of the field and is irreducible polynomial in then can be factored as a product of linear factors in the splitting field. If the polynomial has different roots in the splitting field the polynomial is called polynomial separable. In this study polynomial separable is contained of odd degree in which the coefficients of the tribes polynomial is contained in the extension field. Polynomial is called a polynomial separable odd because it has different roots in the factors and there is one factor in a polynomial in the field. Splitting field that contains all the set of polynomials separable is called normal extension.