Geodesic
Regularity and intersections of bracket powers
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 593-599
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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.
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.
DOI : 10.21136/CMJ.2022.0066-21
Classification : 13A35, 13B40, 13H05
Keywords: regular ring; Ohm-Rush content theory; intersection flat; bracket power; Frobenius endomorphism 
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Epstein, Neil. Regularity and intersections of bracket powers. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 593-599. doi: 10.21136/CMJ.2022.0066-21

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