[Merged by Bors] - feat(ring_theory): define fractional_ideal.adjoin_integral
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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: Ashvni ashvni.n@gmail.com Co-Authored-By: Filippo A. E. Nuccio filippo.nuccio@univ-st-etienne.fr
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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: Ashvni ashvni.n@gmail.com Co-Authored-By: Filippo A. E. Nuccio filippo.nuccio@univ-st-etienne.fr
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This PR shows if
xis integral overR, thenR[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_invimplies that the ring is integrally closed.Co-Authored-By: Ashvni ashvni.n@gmail.com
Co-Authored-By: Filippo A. E. Nuccio filippo.nuccio@univ-st-etienne.fr