Théorie des Ensembles¶
Bourbaki, N. (1958). Théorie des Ensembles: Algèbre. Éléments de Mathématique.
Cited by¶
8 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Abstraction
This source(Tier C — bibliography only; existence verified, Hermann/Paris confirmed.) Structuralist program organizing mathematics around shared abstract 'structures' (sets, groups, rings, topologies). Link-only.
- Associativity
- Bourbaki (1942+) systematized the formal exposition of associativity across abstract algebraic structures in Éléments de Mathématique.
This sourceThe 'Structures' chapter systematizes the structural (axiomatic) exposition of algebraic laws including associativity across abstract structures
- Bourbaki (1942+) systematized the formal exposition of associativity across abstract algebraic structures in Éléments de Mathématique.
- Closure
- … both; a field adds multiplicative inverses for non-zero elements with closure under multiplicative inverse; a vector space over a field requires closure under vector addition and scalar multiplication; a module generalises vector spaces over rings rather than fields, again with closure under module operations.
This sourceModern axiomatic treatment of algebraic structures with closure as a foundational axiom of each layer (magma, semigroup, monoid, group, ring, field, vector space, algebra); the canonical reference for the closure-axiomatic framing of structural algebra.
- … both; a field adds multiplicative inverses for non-zero elements with closure under multiplicative inverse; a vector space over a field requires closure under vector addition and scalar multiplication; a module generalises vector spaces over rings rather than fields, again with closure under module operations.
- Commutativity
This sourceFormal exposition of associativity in abstract algebraic structures.
- Mathematics (core domain): Abelian groups (groups where the operation is commutative); commutative rings (rings where multiplication commutes — including all fields), whose general structure theory Bourbaki (1942–) systematized in Éléments de Mathématique
This sourceSystematic exposition of the structure theory of commutative rings — the correct Bourbaki volume for the body's commutative-ring claim. (Citation-fix: the prior citation pointed to Théorie des Ensembles, the set-theory book, which does not treat commutative rings.)
- Set and Membership
- The Bourbaki collective's
This sourceMulti-volume series. Paris: Hermann, from 1939 onwards (Fascicule I: Théorie des ensembles, 1939; subsequent fascicules on algebra, topology, integration, etc.). Pseudonymous collective authorship; provided the systematic set-theoretic foundation for twentieth-century pure mathematics.
- The Bourbaki collective's
- Well-Foundedness (Well-Ordering)
- These six components compose: a carrier is presented; a strict relation is identified; the well-foundedness condition is verified (or assumed as an axiom); the rank function supplies the ordinal-valued measure; totality may or may not be added; and the use drives the downstream argument — a compositional packaging that Bourbaki (1939) makes explicit in their axiomatic treatment of noetherian (well-founded) induction.
This sourceLong-running mathematical treatise developing the Bourbaki program: abstraction of mathematics into universal structures (sets, groups, rings, topologies, etc.) — a deliberate project to identify the most general structural patterns. Exemplifies systematic abstraction in mathematics.
- These six components compose: a carrier is presented; a strict relation is identified; the well-foundedness condition is verified (or assumed as an axiom); the rank function supplies the ordinal-valued measure; totality may or may not be added; and the use drives the downstream argument — a compositional packaging that Bourbaki (1939) makes explicit in their axiomatic treatment of noetherian (well-founded) induction.
Domain-specific¶
Verification¶
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://link.springer.com/book/10.1007/978-3-540-34035-5 ×1
- https://www.google.com/books/edition/Commutative_Algebra/Bb30CjGW7EAC ×1
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