Library mathcomp.algebra.countalg
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.
Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ssralg.
Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ssralg.
The algebraic part of the algebraic hierarchy for countable types
This file clones part of ssralg hierarchy for countable types; it does
not cover the left module / algebra interfaces, providing only
countNmodType == countable nmodType interface
countZmodType == countable zmodType interface
countSemiRingType == countable semiRingType interface
countRingType == countable ringType interface
countComSemiRingType == countable comSemiRingType interface
countComRingType == countable comRingType interface
countUnitRingType == countable unitRingType interface
countComUnitRingType == countable comUnitRingType interface
countIdomainType == countable idomainType interface
countFieldType == countable fieldType interface
countDecFieldType == countable decFieldType interface
countClosedFieldType == countable closedFieldType interface
This file provides constructions for both simple extension and algebraic
closure of countable fields.
Set Implicit Arguments.
Local Open Scope ring_scope.
Import GRing.Theory CodeSeq.
Module CountRing.
Import GRing.Theory.
#[short(type="countNmodType")]
HB.structure Definition Nmodule := {M of GRing.Nmodule M & Countable M}.
#[short(type="countZmodType")]
HB.structure Definition Zmodule := {M of GRing.Zmodule M & Countable M}.
#[short(type="countSemiRingType")]
HB.structure Definition SemiRing := {R of GRing.SemiRing R & Countable R}.
#[short(type="countRingType")]
HB.structure Definition Ring := {R of GRing.Ring R & Countable R}.
#[short(type="countComSemiRingType")]
HB.structure Definition ComSemiRing := {R of GRing.ComSemiRing R & Countable R}.
#[short(type="countComRingType")]
HB.structure Definition ComRing := {R of GRing.ComRing R & Countable R}.
#[short(type="countUnitRingType")]
HB.structure Definition UnitRing := {R of GRing.UnitRing R & Countable R}.
#[short(type="countComUnitRingType")]
HB.structure Definition ComUnitRing := {R of GRing.ComUnitRing R & Countable R}.
#[short(type="countIdomainType")]
HB.structure Definition IntegralDomain :=
{R of GRing.IntegralDomain R & Countable R}.
#[short(type="countFieldType")]
HB.structure Definition Field := {R of GRing.Field R & Countable R}.
#[short(type="countDecFieldType")]
HB.structure Definition DecidableField :=
{R of GRing.DecidableField R & Countable R}.
#[short(type="countClosedFieldType")]
HB.structure Definition ClosedField := {R of GRing.ClosedField R & Countable R}.
#[export]
HB.instance Definition _ (R : countNmodType) := Nmodule.on R^o.
#[export]
HB.instance Definition _ (R : countZmodType) := Zmodule.on R^o.
#[export]
HB.instance Definition _ (R : countSemiRingType) := SemiRing.on R^o.
#[export]
HB.instance Definition _ (R : countRingType) := Ring.on R^o.
End CountRing.
Import CountRing.