Su di una congettura di Sudbery
In this paper a conjecture of Sudbery concerning the relations between the roots of a polynomial and of its derivatives is disproved and some remarks on the subject are made.
On a classical theorem concerning algebraic systems of hypersurfaces in a projective space or in a projective variety
Viene stabilito in ogni caratteristica l'analogo del cosiddetto Teorema dell'Indice per sistemi algebrici di ipersuperficie di uno spazio proiettivo o di una varietà proiettiva (cfr. B. Segre [9] per il caso della caratteristica zero) e ne vengono tratte alcune applicazioni.
Terne di quadrati consecutivi in un campo di Galois
Explicit formulae for the number of triplets of consecutive squares in a Galois field are given.
On a linearity criterion for algebraic systems of divisors on a projective variety
In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.
Sul tipo di Lenz-Barlotti di certe estensioni di un piano grafico infinito
In this paper the Lenz-Barlotti type of "ultrapowers" of an infinite graphic plane is established.
Terne di quadrati consecutivi in un campo di Galois
Explicit formulae for the number of triplets of consecutive squares in a Galois field are given.
On a linearity criterion for algebraic systems of divisors on a projective variety
In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.
Generalizzazione del concetto di traccia di un endomorfismo
In this Note I we propose, by means of the Grothendieck group , an intrinsic definition of the trace of a vector space endomorphism, particularly convenient in the infinite dimensional case. The following Note II will then establish the connection of our definition with other ones given by different Authors.
Generalizzazione del concetto di traccia di un endomorfismo
Cf. the Summary of Note I, appeared in the previous issue of these «Rendiconti» at p. 115.
On the Gauss-Lucas'lemma in positive characteristic
If is a polynomial with coefficients in the field of complex numbers, of positive degree , then has at least one root a with the following property: if , where is the multiplicity of , then (such a root is said to be a "free" root of ). This is a consequence of the so-called Gauss-Lucas'lemma. One could conjecture that this property remains true for polynomials (of degree ) with coefficients in a field of positive characteristic (Sudbery's Conjecture). In this paper it is shown that,...
On the Gauss-Lucas'lemma in positive characteristic
If is a polynomial with coefficients in the field of complex numbers, of positive degree , then has at least one root a with the following property: if , where is the multiplicity of , then (such a root is said to be a "free" root of ). This is a consequence of the so-called Gauss-Lucas'lemma. One could conjecture that this property remains true for polynomials (of degree ) with coefficients in a field of positive characteristic (Sudbery's Conjecture). In this paper it is shown that,...
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