We characterize the finiteness of degrees of irreducible morphisms between indecomposable modules lying in coils of the Auslander–Reiten quivers of artin algebras. We mainly study non-zero compositions of irreducible ...

We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of their irreducible degrees.

We consider A to be an artin algebra. We study the degrees of irreducible morphisms between modules in Auslander-Reiten components Gamma having only almost split sequences with at most two indecomposable middle terms, ...

This paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete ...

We study how to read from the ordinary quiver of a representation-finite string algebra, the minimal lower bound m ≥ 1 such that the mth power of the radical of its module category vanishes. We also show how to read the ...

We study the degrees of irreducible morphisms between indecomposablemodules lying in generalized standard coherent almost cyclic componentsof Auslander-Reiten quivers of artin algebras.

We study the degree of irreducible morphisms in generalized standard convex components of the Auslander-Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length. ...

Given a finite dimensional algebra A over an algebraically closed field we study the relationship between the powers of the radical of a morphism in the module category of the algebra A and the induced morphism in the ...

Let $\mathbb {F}_{q} $ be a finite field with $ q $ elements. In this thesis, we focus on two types of problems about irreducible polynomials. The first one is the construction of irreducible polynomials from the composition ...