Normalization is a fundamental ring-theoretic operation; geometrically it resolves singularities in codimension one. Existing algorithmic methods for computing the normalization rely on a common recipe: successively enlarge the given ring in form of an endomorphism ring of a certain (fractional) ideal until the process becomes stationary. While Vasconcelos' method uses the dual Jacobian ideal, ...

The paper is devoted to the so-called complete Leibniz algebras. It known that a Lie algebra with ideal split. We will prove this result valid for algebras whose solvable such codimension of nilradical equal number generators nilradical.

In his work on birational classification of foliations projective surfaces, Brunella showed that every regular foliation a rational surface is algebraically integrable with leaves. This led Touzet to conjecture rationally connected manifold Druel proved this for the case weak Fano manifolds. paper, we extend result showing Touzet’s true codimension one threefolds nef anti-canonical bundle.