Theorems · Definition · ring theory

NonUnitalStarSubalgebra.toNonUnitalSubring

{R : Type u} →
  {A : Type v} →
    [inst : CommRing R] →
      [inst_1 : NonUnitalRing A] →
        [inst_2 : Module R A] → [inst_3 : Star A] → NonUnitalStarSubalgebra R A → NonUnitalSubring A

A non-unital star subalgebra over a ring is also a Subring.

Defined in: Mathlib.Algebra.Star.NonUnitalSubalgebra
Cited by: 4 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext
Assumes: CommRing NonUnitalRing Module Star

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Cites9

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

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Starstatement and proof · cited by 496
NonUnitalRingstatement and proof · cited by 422
NonUnitalSubsemiringproof · cited by 201
NonUnitalStarSubalgebrastatement and proof · cited by 196
NonUnitalSubringstatement · cited by 185
NonUnitalStarSubalgebra.toNonUnitalSubalgebraproof · cited by 37
NonUnitalSubalgebra.toNonUnitalSubsemiringproof · cited by 33

Cited by4

Results whose statement or proof uses this declaration.

NonUnitalStarSubalgebra.toNonUnitalSubring_injectivestatement and proof · cited by 1
NonUnitalStarSubalgebra.mem_toNonUnitalSubringstatement · cited by 1
NonUnitalStarSubalgebra.coe_toNonUnitalSubringstatement · cited by 0
NonUnitalStarSubalgebra.toNonUnitalSubring_injstatement · cited by 0