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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A mgmring.xml GAP documentation Thomas Breuer -->
<!-- %% -->
<!-- %% -->
<!-- %Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<Chapter Label="Magma Rings">
<Heading>Magma Rings</Heading>
<#Include Label="[1]{mgmring}">
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Free Magma Rings">
<Heading>Free Magma Rings</Heading>
<#Include Label="FreeMagmaRing">
<#Include Label="GroupRing">
<#Include Label="IsFreeMagmaRing">
<#Include Label="IsFreeMagmaRingWithOne">
<#Include Label="IsGroupRing">
<#Include Label="UnderlyingMagma">
<#Include Label="AugmentationIdeal">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Elements of Free Magma Rings">
<Heading>Elements of Free Magma Rings</Heading>
<#Include Label="[2]{mgmring}">
<#Include Label="IsMagmaRingObjDefaultRep">
<#Include Label="IsElementOfFreeMagmaRing">
<#Include Label="IsElementOfFreeMagmaRingFamily">
<#Include Label="CoefficientsAndMagmaElements">
<#Include Label="ZeroCoefficient">
<#Include Label="ElementOfMagmaRing">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Natural Embeddings related to Magma Rings">
<Heading>Natural Embeddings related to Magma Rings</Heading>
<#Include Label="[3]{mgmring}">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Magma Rings modulo Relations">
<Heading>Magma Rings modulo Relations</Heading>
<#Include Label="[4]{mgmring}">
<#Include Label="IsElementOfMagmaRingModuloRelations">
<#Include Label="IsElementOfMagmaRingModuloRelationsFamily">
<#Include Label="NormalizedElementOfMagmaRingModuloRelations">
<#Include Label="IsMagmaRingModuloRelations">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Magma Rings modulo the Span of a Zero Element">
<Heading>Magma Rings modulo the Span of a Zero Element</Heading>
<#Include Label="IsElementOfMagmaRingModuloSpanOfZeroFamily">
<#Include Label="IsMagmaRingModuloSpanOfZero">
<#Include Label="MagmaRingModuloSpanOfZero">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Technical Details about the Implementation of Magma Rings">
<Heading>Technical Details about the Implementation of Magma Rings</Heading>
<#Include Label="[5]{mgmring}">
</Section>
</Chapter>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->
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