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The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: mathematics, sciences
Examples
- 2003, Ragnar-Olaf Buchweitz, Morita contexts, idempotents, and Hochschild cohomology — with applications to invariant rings, Luchezar L. Avramov, Marcel Morales, Marc Chardin, Claudia Polini (editors), Commutative Algebra: Interactions with Algebraic Geometry: International Conference, American Mathematical Society, page 27, It is not until section 7 that we deal with commutative algebra proper, whereas the sections leading up to it should be seen as advocacy that excursions into noncommutative algebra can help to shed light on problems in commutative algebra.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Any algebra (mathematical structure) in which the multiplication operation is commutative.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Narrower terms: polynomial ring
No etymology was provided for this word.
Across languages
Translations
8 source translations are retained for this English entry.
-
Italian:
algebra commutativa
— branch of mathematics
-
Polish:
algebra przemienna
— branch of mathematics
-
Portuguese:
álgebra comutativa
— branch of mathematics
-
Russian:
коммутати́вная а́лгебра
(kommutatívnaja álgebra)
— branch of mathematics
-
Italian:
algebra commutativa
— algebra in which multiplication is commutative
-
Polish:
algebra przemienna
— algebra in which multiplication is commutative
-
Portuguese:
álgebra comutativa
— algebra in which multiplication is commutative
-
Russian:
коммутати́вная а́лгебра
(kommutatívnaja álgebra)
— algebra in which multiplication is commutative
