feat(ring_theory): define `fractional_ideal.adjoin_integral` (#8296)
feat(ring_theory): define `fractional_ideal.adjoin_integral` (#8296)

This PR shows if `x` is integral over `R`, then `R[x]` is a fractional ideal, and proves some of the essential properties of this fractional ideal.

This is an important step towards showing `is_dedekind_domain_inv` implies that the ring is integrally closed.

Co-Authored-By: 5f4fefc95b76fd2e0db2bc9a32b0a09fa07471d6@gmail.com
Co-Authored-By: 6a0f648794599ad748371b6f4491f2f7bf335c01@univ-st-etienne.fr





leanprover-community/mathlib,leanprover-community/mathlib