[Merged by Bors] - feat(algebra/field, ring_theory/ideal/basic): an ideal is maximal iff the quotient is a field #3986
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an ideal is maximal iff the quotient is a field One half of the theorem was already proven (the implication maximal ideal implies that the quotient is a field), but the other half was not, mainly because it was missing a necessary predicate. I added the predicate is_field that can be used to tell Lean that the usual ring structure on the quotient extends to a field. The predicate along with proofs to move between is_field and field were provided by Kevin Buzzard. I also added a lemma that the inverse is unique in is_field. At the end I also added the iff statement of the theorem.
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predicate was given under square brackets Seems like there is a problem when giving as an argument under square brackets a predicate. I did not get this error on my device and I did try leanproject build. The issue has been fixed along with a few other minor changes to the features of my previous commit.
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Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
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… the quotient is a field (#3986) One half of the theorem was already proven (the implication maximal ideal implies that the quotient is a field), but the other half was not, mainly because it was missing a necessary predicate. I added the predicate is_field that can be used to tell Lean that the usual ring structure on the quotient extends to a field. The predicate along with proofs to move between is_field and field were provided by Kevin Buzzard. I also added a lemma that the inverse is unique in is_field. At the end I also added the iff statement of the theorem. Co-authored-by: AlexandruBosinta <32337238+AlexandruBosinta@users.noreply.github.com>
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… the quotient is a field (#3986) One half of the theorem was already proven (the implication maximal ideal implies that the quotient is a field), but the other half was not, mainly because it was missing a necessary predicate. I added the predicate is_field that can be used to tell Lean that the usual ring structure on the quotient extends to a field. The predicate along with proofs to move between is_field and field were provided by Kevin Buzzard. I also added a lemma that the inverse is unique in is_field. At the end I also added the iff statement of the theorem. Co-authored-by: AlexandruBosinta <32337238+AlexandruBosinta@users.noreply.github.com>
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… the quotient is a field (#3986) One half of the theorem was already proven (the implication maximal ideal implies that the quotient is a field), but the other half was not, mainly because it was missing a necessary predicate. I added the predicate is_field that can be used to tell Lean that the usual ring structure on the quotient extends to a field. The predicate along with proofs to move between is_field and field were provided by Kevin Buzzard. I also added a lemma that the inverse is unique in is_field. At the end I also added the iff statement of the theorem. Co-authored-by: AlexandruBosinta <32337238+AlexandruBosinta@users.noreply.github.com>
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One half of the theorem was already proven (the implication maximal
ideal implies that the quotient is a field), but the other half was not,
mainly because it was missing a necessary predicate.
I added the predicate is_field that can be used to tell Lean that the
usual ring structure on the quotient extends to a field. The predicate
along with proofs to move between is_field and field were provided by
Kevin Buzzard. I also added a lemma that the inverse is unique in
is_field.
At the end I also added the iff statement of the theorem.