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