Commutative algebra. With a view toward algebraic geometry

Eisenbud, D. (1995). Commutative algebra. With a view toward algebraic geometry: with a View Toward Algebraic Geometry. Springer-Verlag.

Type

Book

Intellectual base

Review or monograph

Year

1995

DOI

10.1007/978-1-4612-5350-1

ISBN

9783540781226

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-1-4612-5350-1

Cited by

12 citations across 12 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Associated graded ring
  • The filtration must be multiplicative, quotient representatives require well-defined multiplication and the construction depends on the chosen ideal or filtration.
• Castelnuovo–Mumford Regularity
  • Finitely generated graded modules. Minimal resolutions, Betti tables, local cohomology, and linear truncations give computable equivalent formulations in the standard graded setting.
• Commutative ring
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Connected ring
  • … the distinction between constitutive identity and a convenient observable transfers from Every integral domain is connected because an idempotent e satisfies e(e−1)=0 and hence e is zero or one. to Algebraists distinguish connected from irreducible spectrum and track whether the ring is commutative and unital..
• Depth (ring theory)
  • For a finitely generated module over a commutative Noetherian local ring, depth records how many successive non-zero-divisors can be chosen from the maximal ideal before unavoidable torsion appears.
• Eilenberg–Mazur swindle
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Exact sequence
  • … from A canonical instance directly demonstrates that the category and zero morphisms, ordered objects and maps, and image-equals-kernel condition at every claimed position are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Formal derivative
  • This behavior is a feature of the coefficient ring, not a defect inherited from analysis.

    This sourceGraduate Texts in Mathematics 150. Springer. https://doi.org/10.1007/978-1-4612-5350-1

• Free presentation
  • A free presentation of M is an exact sequence F_1→F_0→M→0 with F_0 and F_1 free, so M is the quotient of generators by the image of relations.
• Normal scheme
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Principal Ideal
  • The preserved Wikipedia revision is discovery provenance only; the identity is grounded in the cited algebra sources.
• Total ring of fractions
  • … so Q(R) is its fraction field; for a product of domains, the total quotient ring is the product of their fraction fields. to In algebraic geometry, rational functions on a reducible affine scheme are modeled componentwise through the total quotient ring while retaining information from all irreducible components..

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