Classes of irreducible polynomials of degree 3 in Q[x]
DOI:
https://doi.org/10.35819/remat2021v7i1id4212Keywords:
Polynomials in Z[x], Ones, Irreducibility Criterion, Equivalence RelationAbstract
In this work we consider polynomials with integer coefficients and study the irreducibility of these polynomials in Q[x]. We will define an equivalence relation over Z[x]\{0} and we will show the polynomials of degree 3 belonging to certain equivalence classes are irreducible in Q[x]. We will also show that, in some cases, the ones of the coefficients of a polynomial determines its class. Finally, we show how we can create irreducible polynomials from a known irreducible polynomial by adding digits to the left of the ones of the coefficients of that polynomial.
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HUNGERFORD, T. W. Abstract Algebra: An Introduction. 3. ed. Boston: Books/Coles Cengage Learning, 2014.
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