Theorems · Theorem · commutative algebra
Subring.map_iSup
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {ι : Sort u_1} (f : R →+* S)
(s : ι → Subring R), Subring.map f (iSup s) = ⨆ i, Subring.map f (s i)- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- iSupstatement · cited by 2,415
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- GaloisConnection.l_iSupproof · cited by 78
- Subring.mapstatement · cited by 33
- Subring.gc_map_comapproof · cited by 7
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