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refactor(RingTheory/HahnSeries) : several generalizations #12251
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Algebra (groups, rings, fields, etc)
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Order theory
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feat (RingTheory/HahnSeries) : refactor
feat (RingTheory/HahnSeries) : generalize
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refactor (RingTheory/HahnSeries) : several generalizations
refactor(RingTheory/HahnSeries) : several generalizations
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This PR is a container for several smaller PRs that refactor and generalize the existing Hahn series theory. It is (I think) all we need from Hahn series to get a palatable theory of vertex algebras off the ground (other prerequisites from Lie algebras will eventually come in a different PR). Major changes include:
orderTop
andleadingCoeff
functions. Here,orderTop
is aWithTop Γ
-valued version oforder
that does not need[Zero Γ]
andleadingCoeff
returns the coefficient of the minimal element of support (or zero if empty).HahnSeries Γ R
-module structure onHahnModule Γ' R V
, whenΓ
is anOrderedCancelAddCommMonoid
,Γ'
is aPartialOrder
withOrderedCancelVAdd Γ Γ'
,R
is a semiring, andV
is anR
-module.AddVal
to a separate file - the underlying function is justorderTop
, but the description of the valuation needs an additional import and anIsDomain
hypothesis. Results that depended onAddVal
are changed to useorderTop
and generalized.