feat(ring_theory/ideals): quotient rings #196
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kbuzzard
reviewed
Jul 15, 2018
| @@ -3,15 +3,44 @@ Copyright (c) 2018 Kenny Lau. All rights reserved. | |||
| Released under Apache 2.0 license as described in the file LICENSE. | |||
| Authors: Kenny Lau | |||
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add Chris Hughes.
Thanks Chris by the way -- I need this for perfectoids!
digama0
reviewed
Jul 16, 2018
ring_theory/ideals.lean
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| lemma mul_left {S : set α} [is_ideal S] : b ∈ S → a * b ∈ S := @is_submodule.smul α α _ _ _ _ a _ | ||
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| lemma mul_right {S : set α} [is_ideal S] : a ∈ S → a * b ∈ S := mul_comm b a ▸ mul_left |
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At least zero, add and sub should be protected here.
digama0
reviewed
Jul 16, 2018
ring_theory/ideals.lean
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| /- quotient by maximal ideal is a field. def rather than instance, since users will have | ||
| computable inverses in some applications -/ | ||
| noncomputable def field (S : set α) [is_maximal_ideal S] : field (quotient S) := |
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Quotient rings are a ring, quotient by prime ideal is an integral domain, and quotient by maximal ideal is a field (noncomputable).