About: Subdirect product

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In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944 and has proved to be a powerful generalization of the notion of direct product.

Attributes	Values
rdfs:label	Subdirektes Produkt (de) Iloczyn podprosty (pl) Subdirect product (en)
rdfs:comment	In der universellen Algebra ergibt sich das Problem, dass nicht alle (universellen) Algebren als direktes Produkt direkt irreduzibler Algebren dargestellt werden können. Als Lösung bietet sich das sogenannte subdirekte Produkt an, eine bestimmte Art einer Unteralgebra eines direkten Produktes. Der erste Darstellungssatz von Garrett Birkhoff besagt dann, dass sich jede Algebra als subdirektes Produkt subdirekt irreduzibler Algebren schreiben lässt. (de) In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944 and has proved to be a powerful generalization of the notion of direct product. (en) Iloczyn podprosty – w algebrze abstrakcyjnej (w tym algebrze uniwersalnej, teorii grup, teorii pierścieni i teorii modułów) taka podalgebra , która w całości zależy od wszystkich jej czynników, ale niekoniecznie stanowi ich pełny iloczyn prosty. Pojęcie zostało wprowadzone przez w 1944 roku, okazawszy się potężnym uogólnieniem iloczynu prostego. (pl)
dcterms:subject	Universal algebra
Wikipage page ID	17395221 (xsd:integer)
Wikipage revision ID	954550191 (xsd:integer)
Link from a Wikipage to another Wikipage	Universal algebra Vector space Universal algebra Mathematics Garrett Birkhoff Module theory Complemented lattice Perfect group Distributive lattice Subdirectly irreducible algebra Cyclic group Direct product Goursat's lemma Ring theory Group (mathematics) Heyting algebra Surjective Abelian group Abstract algebra Bulletin of the AMS Group theory Semidirect product Semilattice Subalgebra Subdirect irreducible
Link from a Wikipage to an external page	https://archive.org/details/perfectgroups0000holt
sameAs	Subdirect product Subdirect product Subdirect product Subdirect product Subdirect product
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Fact dbt:Harv
has abstract	In der universellen Algebra ergibt sich das Problem, dass nicht alle (universellen) Algebren als direktes Produkt direkt irreduzibler Algebren dargestellt werden können. Als Lösung bietet sich das sogenannte subdirekte Produkt an, eine bestimmte Art einer Unteralgebra eines direkten Produktes. Der erste Darstellungssatz von Garrett Birkhoff besagt dann, dass sich jede Algebra als subdirektes Produkt subdirekt irreduzibler Algebren schreiben lässt. (de) In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944 and has proved to be a powerful generalization of the notion of direct product. (en) Iloczyn podprosty – w algebrze abstrakcyjnej (w tym algebrze uniwersalnej, teorii grup, teorii pierścieni i teorii modułów) taka podalgebra , która w całości zależy od wszystkich jej czynników, ale niekoniecznie stanowi ich pełny iloczyn prosty. Pojęcie zostało wprowadzone przez w 1944 roku, okazawszy się potężnym uogólnieniem iloczynu prostego. (pl)
gold:hypernym	Subalgebra
prov:wasDerivedFrom	wikipedia-en:Subdirect_product?oldid=954550191&ns=0
page length (characters) of wiki page	4401 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Subdirect_product
is Link from a Wikipage to another Wikipage of	Łukasiewicz–Moisil algebra Distributive lattice Irreducible ring Subdirectly irreducible algebra Noncommutative ring Goursat's lemma Von Neumann regular ring Semidirect product Skew lattice Rubik's Cube group Semiprimitive ring
is foaf:primaryTopic of	wikipedia-en:Subdirect_product

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