Add to ORKGAbstract. In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over Q which are not of Eisenstein type. 1
On the irreducibility of some polynomials in two variables by B. Brindza and Á. Pintér (Debrecen) ...
AbstractLet K be a field of characteristic 0. We produce families of polynomials f(x,y), irreducible...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
Abstract. In [4] we showed that a polynomial over a Noetherian ring is divisible by some other polyn...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
One of the results generalizing Eisenstein Irreducibility Criterion states that if φ(x) = anxn+...
One of the results generalizing Eisenstein Irreducibility Criterion states that if φ(x) = anxn+...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irredu...
A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial i...
AbstractWe prove a criterion for the irreducibility of the polynomials in one indeterminate with the...
Let R be a commutative ring with a unit element, F(x) a homogeneous polynomial of degree n in t inde...
In 1956, Ehrenfeucht proved that a polynomial f <SUB>1</SUB>(x <SUB>1</SUB>) + · + f <SUB>n</SUB> (x...
In many mathematical investigations such as determination of degree of a field extension, determinat...
On the irreducibility of some polynomials in two variables by B. Brindza and Á. Pintér (Debrecen) ...
AbstractLet K be a field of characteristic 0. We produce families of polynomials f(x,y), irreducible...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
Abstract. In [4] we showed that a polynomial over a Noetherian ring is divisible by some other polyn...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
One of the results generalizing Eisenstein Irreducibility Criterion states that if φ(x) = anxn+...
One of the results generalizing Eisenstein Irreducibility Criterion states that if φ(x) = anxn+...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irredu...
A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial i...
AbstractWe prove a criterion for the irreducibility of the polynomials in one indeterminate with the...
Let R be a commutative ring with a unit element, F(x) a homogeneous polynomial of degree n in t inde...
In 1956, Ehrenfeucht proved that a polynomial f <SUB>1</SUB>(x <SUB>1</SUB>) + · + f <SUB>n</SUB> (x...
In many mathematical investigations such as determination of degree of a field extension, determinat...
On the irreducibility of some polynomials in two variables by B. Brindza and Á. Pintér (Debrecen) ...
AbstractLet K be a field of characteristic 0. We produce families of polynomials f(x,y), irreducible...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...