feat: bring algebras into shape

- documentation
- tests
- renaming

docs/src/.vitepress/config.mts

@@ -88,6 +88,14 @@ export default defineConfig({
                 { text: 'Discriminant groups', link: 'manual/quad_forms/discriminant_group'},
               ]
             },
+            { text: 'Algebras',
+              collapsed: true,
+              items: [
+                { text: 'Introduction', link: 'manual/algebras/intro'},
+                { text: 'Basics', link: 'manual/algebras/basics'},
+                { text: 'Structure constant algebras', link: 'manual/algebras/structureconstant'},
+              ]
+            },
             {
               text: 'Elliptic curves',
               collapsed: true,

src/AlgAss.jl

@@ -1,7 +1,7 @@
 include("AlgAss/Map.jl")
 include("AlgAss/AbsAlgAss.jl")
 include("AlgAss/AlgQuat.jl")
-include("AlgAss/AlgAss.jl")
+include("AlgAss/StructureConstantAlgebra.jl")
 include("AlgAss/radical.jl")
 include("AlgAss/ChangeRing.jl")
 include("AlgAss/AlgGrp.jl")

src/AlgAss/AbsAlgAss.jl

@@ -1,5 +1,22 @@
 _base_ring(A::AbstractAssociativeAlgebra) = base_ring(A)
 
+# document the following
+#base_ring
+#zero_algebra(T,...)
+#iszero
+#has_one
+#dim
+#@doc raw"""
+#    is_commutative(A::StructureConstantAlgebra) -> Bool
+#
+#Returns `true` if $A$ is a commutative ring and `false` otherwise.
+#"""
+#raw"""
+#    zero_algebra(R::Ring) -> StructureConstantAlgebra
+#
+#Return the zero ring as an associative $R$-algebra.
+#"""
+
 ################################################################################
 #
 #  Morphism types