Theorems · Theorem · commutative algebra
FractionalIdeal.coe_mul
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
(I J : FractionalIdeal S P), ↑(I * J) = ↑I * ↑J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submodulestatement · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
- FractionalIdeal.mul_defproof · cited by 6
Cited by16
Results whose statement or proof uses this declaration.
- FractionalIdeal.spanSingleton_mul_spanSingletonproof · cited by 11
- FractionalIdeal.den_mul_self_eq_num'proof · cited by 5
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.le_div_iff_mul_leproof · cited by 3
- FractionalIdeal.coeSubmoduleHomproof · cited by 2
- FractionalIdeal.le_dual_iffproof · cited by 2
- FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulproof · cited by 1
- FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_topproof · cited by 1
- FractionalIdeal.dual_eq_dual_mul_dualproof · cited by 1
- FractionalIdeal.mul_one_div_le_oneproof · cited by 1
- conductor_mul_differentIdealproof · cited by 1
- FractionalIdeal.le_self_mul_one_divproof · cited by 1