Algebra I

Bourbaki, N. (1989). Algebra I: Chapters 1–3. Springer.

Type

Book

Intellectual base

Review or monograph

Year

1989

Pages cited

1-3

DOI

10.1007/978-3-642-61698-3

ISBN

9783540007067

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-3-642-61698-3

Cited by

5 citations across 5 artifacts.

Domain-specific

• Exterior Algebra
  • The construction packages all finite alternating multilinear combinations of elements of `M` into one associative, unital, graded algebra.
• Multilinear form
  • The correspondence preserves the two-slot structure without confusing the Cartesian product with a tensor product.
• Product of Rings
  • Coordinate projections \(\pi_i:R\to R_i\) make it the categorical product: every compatible family of ring homomorphisms \(f_i:S\to R_i\) factors through one unique \(f:S\to R\).
• Semilinear map
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Transpose of a linear map
  • … that the field, domain and codomain, original linear map, chosen algebraic or continuous duals, pullback formula, pairing identity, continuity assumptions and basis representation are explicit. to An applied instance preserves the same invariant under changed notation, scale, jurisdiction, dataset, or implementation..

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