Über die Theorie der algebraischen Formen

Hilbert, D. (1890). Über die Theorie der algebraischen Formen. Mathematische Annalen, 473-534.

Type

Journal article

Intellectual base

Primary research

Year

1890

DOI

10.1007/bf01208503

Link

https://doi.org/10.1007/BF01208503

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

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

Primes

• Associativity
  • … (core domain)**: Semigroup, monoid, and group theory (associativity is foundational, formalized in 19th-century abstract algebra); ring and field theory (both multiplication and addition must associate, defined explicitly in formal axiomatic systems from Hilbert (1890) onward in his treatment of algebraic forms

    This sourceThe work exists and is foundational to commutative algebra, but it is a paper on invariant theory and algebraic forms, NOT on the axiomatization of associativity in ring/field theory

• Commutativity
  • The distinction between commutative and non-commutative structures shapes enormous amounts of modern mathematics (commutative algebra / algebraic geometry on one side; non-commutative algebra / representation theory / non-commutative geometry on the other), with foundational expositions traceable to Hilbert's (1890) "Über die Theorie der algebraischen Formen" on invariant theory and commutative algebra

    This sourceProves the basis theorem and the syzygy theorem, foundational to invariant theory and commutative algebra — supports the claim that foundational expositions trace to Hilbert's invariant-theory / commutative-algebra work.

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