arXiv subjects
Publications and source records attributed to Juan Pablo Acosta López.
We show that the 1-h-minimal fields satisfy a property of naive compactness for decreasing definable families of closed bounded sets indexed by the value group. We use this to prove that a local topological definable group has a definable family of neighborhoods of the identity consisting of open subgroups.
We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.
A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.
In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew $PBW$ extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others. As a corollary we will give a new short proof of the Poincaré-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras.