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Fix up generic characteristic method for localized rings. #4346

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Nov 25, 2024
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Fix up generic characteristic method for localized rings. #4346

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10 changes: 9 additions & 1 deletion src/Rings/localization_interface.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -399,7 +399,15 @@

canonical_unit(f::LocRingElemType) where {LocRingElemType<:AbsLocalizedRingElem} = one(parent(f))

characteristic(W::AbsLocalizedRing) = characteristic(base_ring(W))
function characteristic(W::AbsLocalizedRing)
# It might happen that localization collapses the ring.
is_zero(one(W)) && return 1
# If the characteristic is prime, then it is preserved.
c = characteristic(base_ring(W))
(is_zero(c) || is_prime(c)) && return c
# All other cases have to be overwritten manually.
error("computation of characteristic not implemented")

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end

function Base.show(io::IO, ::MIME"text/plain", W::AbsLocalizedRing)
io = pretty(io)
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