Degrees of irreducible morphisms and finite-representation type

Degrees of irreducible morphisms and finite-representation type

We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the ...

On Finite Groups With Two Irreducible Character Degrees

on finite groups with two irreducible character degrees

Distribution of irreducible polynomials of small degrees over finite fields

D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan’s work. For a prime power q let Fq denote the finite field of order q. Hansen and Mullen in [4, p. 6...

DEGREES OF IRREDUCIBLE PROJECTIVE REPRESENTATIONS OF FINITE GROUPSf

where St and S2 are projective representations of G. An irreducible projective representation is one that is not reducible. In this paper, we study the degrees of irreducible projective representations of a finite group G over an algebraically closed field K. In Theorem 2, we require further that char KJ(\G\. The degree of an irreducible projective representation of a finite group G, over the c...