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Commit 2021-08-16 16:19 80b699bc

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chore(ring_theory): generalize non_zero_divisors lemmas to monoid_with_zero (#8607) None of the results about non_zero_divisors needed a ring structure, just a monoid_with_zero. So the generalization is obvious. Shall we move this file to the algebra namespace sometime soon?

Estimated changes

Modified src/ring_theory/ideal/over.lean

Modified src/ring_theory/jacobson.lean

Modified src/ring_theory/localization.lean

Modified src/ring_theory/non_zero_divisors.lean

modified theorem eq_zero_of_ne_zero_of_mul_left_eq_zero

modified theorem eq_zero_of_ne_zero_of_mul_right_eq_zero

deleted theorem le_non_zero_divisors_of_domain

added theorem le_non_zero_divisors_of_no_zero_divisors

deleted theorem map_le_non_zero_divisors_of_injective

deleted theorem map_mem_non_zero_divisors

deleted theorem map_ne_zero_of_mem_non_zero_divisors

modified theorem mem_non_zero_divisors_iff_ne_zero

added theorem monoid_with_zero_hom.map_le_non_zero_divisors_of_injective

added theorem monoid_with_zero_hom.map_mem_non_zero_divisors

added theorem monoid_with_zero_hom.map_ne_zero_of_mem_non_zero_divisors

modified theorem mul_mem_non_zero_divisors

deleted theorem powers_le_non_zero_divisors_of_domain

added theorem powers_le_non_zero_divisors_of_no_zero_divisors

modified theorem prod_zero_iff_exists_zero

added theorem ring_hom.map_le_non_zero_divisors_of_injective

added theorem ring_hom.map_mem_non_zero_divisors

added theorem ring_hom.map_ne_zero_of_mem_non_zero_divisors

Modified src/ring_theory/polynomial/scale_roots.lean