The valuation on a quotient ring #
The support of a valuation v : Valuation R Γ₀
is supp v
. If J
is an ideal of R
with h : J ⊆ supp v
then the induced valuation
on R / J
= Ideal.Quotient J
is onQuot v h
.
If hJ : J ⊆ supp v
then onQuotVal hJ
is the induced function on R / J
as a function.
Note: it's just the function; the valuation is onQuot hJ
.
Instances For
The extension of valuation v
on R
to valuation on R / J
if J ⊆ supp v
.
Instances For
The quotient valuation on R / J
has support (supp v) / J
if J ⊆ supp v
.
If hJ : J ⊆ supp v
then onQuotVal hJ
is the induced function on R / J
as a function.
Note: it's just the function; the valuation is onQuot hJ
.
Instances For
The extension of valuation v
on R
to valuation on R / J
if J ⊆ supp v
.
Instances For
The quotient valuation on R / J
has support (supp v) / J
if J ⊆ supp v
.