Khalid Benabdallah

On torsion abelian groups like modules

In [4] Singh started the study of modules MR satisfying the following two conditions: (I) Every finitely generated submodule of any homomorphic image of MR is a direct sum of uniserial modules. (II) Given two uniserial submodules U and V of a homomorphic image of M, for any submodule W of U, any homomorphism f: W → V can be extended to a homomorphism g: U → V provided the composition length d(U/W) ≤ d(V/f(W)).

Orbits of invariant subspaces of algebraic linear operators

Abstract Let E be a vector space over a field K , and A an algebraic K -linear operator on E . We describe the orbits under the action of the commutant of A and of the group of the invertible elements of the commutant of A on the lattice of A -invariant subspaces.