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Keywords:
regular ring; Ohm-Rush content theory; intersection flat; bracket power; Frobenius endomorphism
regular ring; Ohm-Rush content theory; intersection flat; bracket power; Frobenius endomorphism
Summary:
Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence. Connections are made with Ohm-Rush content theory, intersection-flatness of the Frobenius map, and various flatness criteria.
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