Theorems · Theorem · commutative algebra
Ring.HasFiniteQuotients.of_module_finite
∀ (R : Type u_1) [inst : CommRing R] [Ring.HasFiniteQuotients R] (S : Type u_2) [inst_2 : CommRing S] [IsDomain S] [inst_4 : Algebra R S] [Module.Finite R S], Ring.HasFiniteQuotients S
Assume that R has finite quotients and that S is a domain and a finite R-module. Then
S has finite quotients.
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- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Finiteproof · cited by 3,029
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- IsDomainstatement and proof · cited by 2,196
- Module.Finitestatement and proof · cited by 1,032
- Ideal.underproof · cited by 170
- subsingleton_or_nontrivialproof · cited by 161
- Ring.HasFiniteQuotientsstatement and proof · cited by 19
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