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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.

Reine lokale Ringe der Dimension zwei.

Hubert Flenner (1975)

Mathematische Annalen

Relative Buchsbaumness of bigraded modules

Keivan Borna, Ahad Rahimi, Syrous Rasoulyar (2012)

Colloquium Mathematicae

We study finitely generated bigraded Buchsbaum modules over a standard bigraded polynomial ring with respect to one of the irrelevant bigraded ideals. The regularity and the Hilbert function of graded components of local cohomology at the finiteness dimension level are considered.

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Racines approchées, suites génératrices, suffisance des jets

Rank two Ulrich modules over the affine cone of the simple node.

Rationalité des Singularités Canoniques.

Real closures of commutative rings. II.

Real spectra of complete local rings.

Reciprocal domains and Cohen-Macaulay $d$ -complexes in $ℝ^{d}$ .

Reduction numbers, Briançon-Skoda theorems and the depth of Rees rings

Reduction of isolated singularities.

Reflective functions on p-adic fields

Regular Sequences in Rees and Symmetric Algebras I.

Regular Sequences in Rees and Symmetric Algebras II.

Regularity and intersections of bracket powers

Reine lokale Ringe der Dimension zwei.

Relative Buchsbaumness of bigraded modules

Remarks on Blowing-Up Divisorial Ideals.

Remarks on Noetherian local domains of dim 2.

Remarks on reflexive modules, covers, and envelopes.

Residual intersections.

Résultats récents sur l'approximation des morphismes en algèbre commutative

Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay-Moduln.

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