English
An injective non-unital ring homomorphism F: R → S into a NormedRing S induces a NormedRing on R via the norm pulled back along F.
Русский
Инъективный неаддитивный кольцевой однородник F: R → S в NormedRing S индуцирует NormedRing на R через вытягивание нормы по F.
LaTeX
$$$\\text{NormedRing.induced}\\;R\\;S\\;f\\;\\text{(инъективен)}$$
Lean4
/-- An injective non-unital ring homomorphism from a `Ring` to a `NormedRing` induces a
`NormedRing` structure on the domain.
See note [reducible non-instances] -/
abbrev induced [Ring R] [NormedRing S] [NonUnitalRingHomClass F R S] (f : F) (hf : Function.Injective f) :
NormedRing R :=
{ NonUnitalSeminormedRing.induced R S f, NormedAddCommGroup.induced R S f hf, ‹Ring R› with }
