AbstractWe provide a concrete description of some factor rings of the polynomial ring k[X], k a field, as fields of matrices, namely of the factor rings k[X]/(Xn−X−1) for which n is such that the polynomial Xn−X−1 is irreducible in k[X]. These factor rings include the Galois fields GF(pn) for which Xn−X−1 is irreducible in Zp[X]. Both MAGMA and MAPLE show that there are many such fields
Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in crypto...
In this paper we present some algorithms for computing an irreducible decomposition of an ideal in a...
AbstractIt is known that univariate polynomials over finite local rings factor uniquely into primary...
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based o...
AbstractThe paper is concerned with the structure of irreducible polynomials in one variable over a ...
AbstractA matrix A ϵ Mn(F), F an arbitrary field with characteristic p (not necessarily positive), i...
AbstractWe consider the matrix well-known representation of K[X]/(P), when P is monic irreducible po...
Let k be a field with characteristic p and K be a Galois extension of k, the order of the Galois gro...
AbstractLet F be a field of characteristic zero, and let Mn(F) be the algebra of n × n matrices over...
In many mathematical investigations such as determination of degree of a field extension, determinat...
AbstractWe study the factorization of polynomials of the form Fr(x)=bxqr+1−axqr+dx−c over the finite...
AbstractLet Fn denote the ring of n×n matrices over the finite field F=GF(q) and let A(x)=ANxN+ ⋯+ A...
AbstractLet GF(q) be the finite field of order q, let Q(x) be an irreducible polynomial in GF(q)(x),...
In this work, a new construction based on companion matrices of primitive polynomials is provided. G...
AbstractLet A be a given n × n matrix with rational entries and irreducible characteristic polynomia...
Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in crypto...
In this paper we present some algorithms for computing an irreducible decomposition of an ideal in a...
AbstractIt is known that univariate polynomials over finite local rings factor uniquely into primary...
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based o...
AbstractThe paper is concerned with the structure of irreducible polynomials in one variable over a ...
AbstractA matrix A ϵ Mn(F), F an arbitrary field with characteristic p (not necessarily positive), i...
AbstractWe consider the matrix well-known representation of K[X]/(P), when P is monic irreducible po...
Let k be a field with characteristic p and K be a Galois extension of k, the order of the Galois gro...
AbstractLet F be a field of characteristic zero, and let Mn(F) be the algebra of n × n matrices over...
In many mathematical investigations such as determination of degree of a field extension, determinat...
AbstractWe study the factorization of polynomials of the form Fr(x)=bxqr+1−axqr+dx−c over the finite...
AbstractLet Fn denote the ring of n×n matrices over the finite field F=GF(q) and let A(x)=ANxN+ ⋯+ A...
AbstractLet GF(q) be the finite field of order q, let Q(x) be an irreducible polynomial in GF(q)(x),...
In this work, a new construction based on companion matrices of primitive polynomials is provided. G...
AbstractLet A be a given n × n matrix with rational entries and irreducible characteristic polynomia...
Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in crypto...
In this paper we present some algorithms for computing an irreducible decomposition of an ideal in a...
AbstractIt is known that univariate polynomials over finite local rings factor uniquely into primary...
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