Commit 2024-10-04 10:12 12bdcfbb
View on Github →feat(RingTheory): target local closure of property of ring homomorphisms (#17032)
If P
is a property of ring homomorphisms, we call Locally P
the closure of P
with
respect to standard open coverings on the (algebraic) target (i.e. geometric source). Hence
for f : R →+* S
, the property Locally P
holds if it holds locally on S
, i.e. if there exists
a subset { t }
of S
generating the unit ideal, such that P
holds for all compositions
R →+* Sₜ
.
By construction, Locally P
is local on the target. Moreover, stability properties of P
are inherited by Locally P
(TODO).