Theorems · Theorem · ring theory
StarSubalgebra.toSubalgebra_eq_top
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] {S : StarSubalgebra R A},
S.toSubalgebra = ⊤ ↔ S = ⊤- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- StarRingstatement and proof · cited by 1,686
- Subalgebrastatement · cited by 1,353
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarSubalgebra.toSubalgebrastatement · cited by 58
- StarSubalgebra.toSubalgebra_injectiveproof · cited by 3
- StarSubalgebra.top_toSubalgebraproof · cited by 2
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