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Note on the coincidence of two henselisations
María Emilia Alonso García, Henri Lombardi, Stefan Neuwirth
We compare two henselisations of a residually discrete valuation domain. Our constructive proof that a certain natural morphism is an isomorphism is also a proof in classical mathe…
Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings
Stefan Neuwirth, Henri Lombardi, Ihsen Yengui
Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of lead…
Valuative dimension, constructive points of view
Stefan Neuwirth, Henri Lombardi, Ihsen Yengui
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent…
Multivariate Hensel Lemma for ultrametric fields
M. -E. Alonso, H. Lombardi, S. Neuwirth
The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situa…