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  1.  32
    Henselian Valued Fields: A Constructive Point of View.Hervé Perdry - 2005 - Mathematical Logic Quarterly 51 (4):400-416.
    This article is a logical continuation of the Henri Lombardi and Franz-Viktor Kuhlmann article [9]. We address some classical points of the theory of valued fields with an elementary and constructive point of view. We deal with Krull valuations, and not simply discrete valuations. First of all, we show how to construct the Henselization of a valued field; we restrict to fields in which one has at one's disposal algorithmic tools to test the nullity or the valuation ring membership. It (...)
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  2.  16
    Elementary Constructive Theory of Henselian Local Rings.María E. Alonso, Henri Lombardi & Hervé Perdry - 2008 - Mathematical Logic Quarterly 54 (3):253-271.
    We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.
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    Lazy Bases: A Minimalist Constructive Theory of Noetherian Rings.Hervé Perdry - 2008 - Mathematical Logic Quarterly 54 (1):70-82.
    We give a constructive treatment of the theory of Noetherian rings. We avoid the usual restriction to coherent rings; we can even deal with non-discrete rings. We introduce the concept of rings with certifiable equality which covers discrete rings and much more. A ring R with certifiable equality can be fitted with a partial ideal membership test for ideals of R. Lazy bases of ideals of R [X ] are introduced in order to derive a partial ideal membership test for (...)
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  4. Elementary Constructive Theory of Henselian Local Rings.María Emilia Alonso García, Henri Lombardi & Hervé Perdry - 2008 - Mathematical Logic Quarterly 54 (3):253-271.
     
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