In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion ...

In this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If is a nilpotent element of index n with von Neumann regular , we decompose with a Jordan ...

We define H-fibration sequences as fibrations where the holonomy action of the fundamental group of the base on the fiber lies in a given subgroup H of E(F ), where E(F ) is the homotopy automorphism group of the fiber. ...

The aim of this paper is to show how we can induce contact structures, contact metric structures and Sasaki structures on a null hypersurface from a rigging vector field. We give several explicit examples of this construction ...

For any n ≥ 2 and fixed k ≥ 1, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring Mn(F) to be written as a sum of an invertible matrix U and a nilpotent matrix N with Nk ...

Let D denote the unit disc in C. We define the generalized Cesàro operator as follows: Cω( f )(z) = 1 0 f (t z) 1 z z 0 Bω t (u) du ω(t)dt, where {Bω ζ }ζ∈D are the reproducing kernels of the Bergman space ...

We study some properties of the Gelfand-Kirillov dimension in a non-necessarily unital context. In particular, its Morita invariance when the algebras have local units, and its commutativity with direct limits. We then ...

It is known that the ideals of a Leavitt path algebra LK (E) generated by Pl(E), by Pc(E) or by Pec(E) are invariant under isomorphism. Though the ideal generated by Pb∞ (E) is not invariant we find its “natural” replacement ...

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization ...

Let F be a field. We show that given any nth degree monic polynomial q(x) ∈ F[x] and any matrix A ∈ Mn(F) whose trace coincides with the trace of q(x) and consisting in its main diagonal of k 0-blocks of order one, with k ...