Splitting in integral extensions, Cohen-Macaulay modules and algebras

DOI10.1016/0021-8693(88)90200-1zbMath0656.13006OpenAlexW2024617999MaRDI QIDQ1109826

Frank Ma

Publication date: 1988

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90200-1

zbMATH Keywords

ring extensionbig Cohen-Macaulay algebrasdirect summand problemexistence of Cohen-Macaulay modulessplinter

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Extension theory of commutative rings (13B02)

Related Items (11)

On the behavior of \(F\)-signatures, splitting primes, and test modules under finite covers ⋮ On the canonical, fpqc, and finite topologies on affine schemes. The state of the art ⋮ On the Cohen-Macaulay modules of graded subrings ⋮ On some permanence properties of (derived) splinters ⋮ Algebraic geometry in mixed characteristic ⋮ Openness of splinter loci in prime characteristic ⋮ Maximal Cohen–Macaulay modules over certain Segre products ⋮ Koh like theorems for polynomials in mixed characteristic ⋮ Galois extensions, plus closure, and maps on local cohomology ⋮ Absolute integral closures are big Cohen-Macaulay algebras in characteristic 𝑃 ⋮ Tight closure and elements of small order in integral extensions

Cites Work

• The purity of the Frobenius and local cohomology
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Homological dimensions and Macaulay rings
• F-Purity and Rational Singularity
• R-SEQUENCES AND INDETERMINATES
• Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
• Contracted ideals from integral extensions of regular rings
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