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Theorems · Definition · ring theory

subalgebraOfSubring

{R : Type u_1} → [inst : Ring R] → Subring R → Subalgebra ℤ R

A subring is a ℤ-subalgebra.

Defined in
Mathlib.Algebra.Algebra.Subalgebra.Basic
Cited by
5 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
Ring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.adjoin_int · cited by 2Algebra.adjoin_intmem_subalgebraOfSubring · cited by 0mem_subalgebraOfSubringsubalgebraOfSubring_toSubsemiring · cited by 0subalgebraOfSubring_toSub…Subring.closureEquivAdjoinInt · cited by 0Subring.closureEquivAdjoi…is_noetherian_subring_closure · cited by 0is_noetherian_subring_clo…NonUnitalSubring.unitization_range · cited by 0NonUnitalSubring.unitizat…Ring · cited by 7463RingSubalgebra · cited by 1353SubalgebraSubring · cited by 602SubringSubring.toSubsemiring · cited by 71Subring.toSubsemiringsubalgebraOfSubringCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.