About: Change of rings

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In algebra, given a ring homomorphism , there are three ways to change the coefficient ring of a module; namely, for a left R-module M and a left S-module N, * , the induced module. * , the coinduced module. * , the restriction of scalars. They are related as adjoint functors: and This is related to Shapiro's lemma.

Attributes	Values
rdf:type	Thing
rdfs:label	Restriktion und Erweiterung der Skalare (de) Change of rings (en) 係数環の変更 (ja)
rdfs:comment	Die Restriktion der Skalare und die Erweiterung der Skalare sind zwei Methoden aus der Algebra, die es ermöglichen, den Ring eines Moduls zu ändern, das heißt ein -Modul wird in ein -Modul mittels eines Ringhomomorphismus transformiert und aus einem -Modul wird ein -Modul. Aus kategorientheoretischer Sicht handelt sich um einen links- und rechtsadjungierten Funktor zwischen den Kategorien der -Moduln und -Moduln. In der algebraischen Geometrie wird oft die Weil-Restriktion als Restriktion der Skalare bezeichnet. (de) In algebra, given a ring homomorphism , there are three ways to change the coefficient ring of a module; namely, for a left R-module M and a left S-module N, * , the induced module. * , the coinduced module. * , the restriction of scalars. They are related as adjoint functors: and This is related to Shapiro's lemma. (en) 代数学において，環準同型 f: R → S が与えられると，加群の係数環を変更する3つの方法がある；すなわち，右 R-加群 M と右 S-加群 N に対し， * , 誘導加群． * , 余誘導加群． * , 係数の制限．それらは随伴関手として関係する：これはと関係する． (ja)
rdfs:seeAlso	Tensor product of modules
dcterms:subject	Ring theory Adjoint functors Commutative algebra
Wikipage page ID	41410139 (xsd:integer)
Wikipage revision ID	1075016004 (xsd:integer)
Link from a Wikipage to another Wikipage	Canonical map Quaternion Module (mathematics) Representation theory Algebra representation Characteristic polynomial Vector space Ring theory Complex number Complexification Function composition Commutative ring Functor Identity element Functorial Adjoint functors Division algebra Irreducible representation Linear complex structure Adjoint functor Algebraic geometry Nicolas Bourbaki Isomorphism Tensor product of modules Weil restriction Abelian group Commutative algebra Abstract algebra Bimodule Tensor product of fields Associative algebra Degree of a field extension Group representation Group ring Category theory Real number Six operations Shapiro's lemma Tensor-hom adjunction Ring homomorphism Right adjoint Left adjoint dbr:Quaternionification
Link from a Wikipage to an external page	https://archive.org/details/abstractalgebra00dumm_304%7Curl-access=limited%7Clast=Dummit%7Cfirst=David%7Cdate=2004%7Cpublisher=Wiley%7Cothers=Foote, https://archive.org/details/abstractalgebra00dumm_304/page/n372 https://mathoverflow.net/q/1534 http://www.math.uchicago.edu/~may/MISC/TorExt.pdf
sameAs	Change of rings Change of rings Change of rings Change of rings Change of rings Change of rings Change of rings
dbp:wikiPageUsesTemplate	dbt:Repetition dbt:Cite_book dbt:Empty_section dbt:See_also dbt:Sfn
has abstract	Die Restriktion der Skalare und die Erweiterung der Skalare sind zwei Methoden aus der Algebra, die es ermöglichen, den Ring eines Moduls zu ändern, das heißt ein -Modul wird in ein -Modul mittels eines Ringhomomorphismus transformiert und aus einem -Modul wird ein -Modul. Aus kategorientheoretischer Sicht handelt sich um einen links- und rechtsadjungierten Funktor zwischen den Kategorien der -Moduln und -Moduln. In der algebraischen Geometrie wird oft die Weil-Restriktion als Restriktion der Skalare bezeichnet. (de) In algebra, given a ring homomorphism , there are three ways to change the coefficient ring of a module; namely, for a left R-module M and a left S-module N, * , the induced module. * , the coinduced module. * , the restriction of scalars. They are related as adjoint functors: and This is related to Shapiro's lemma. (en) 代数学において，環準同型 f: R → S が与えられると，加群の係数環を変更する3つの方法がある；すなわち，右 R-加群 M と右 S-加群 N に対し， * , 誘導加群． * , 余誘導加群． * , 係数の制限．それらは随伴関手として関係する：これはと関係する． (ja)
prov:wasDerivedFrom	wikipedia-en:Change_of_rings?oldid=1075016004&ns=0
page length (characters) of wiki page	8788 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Change_of_rings
is rdfs:seeAlso of	Frobenius reciprocity
is Link from a Wikipage to another Wikipage of	Restriction of scalars Glossary of ring theory Frobenius reciprocity Fundamental theorem of algebraic K-theory Extension of scalars Coinduced module Ring (mathematics) Tropical geometry Associative algebra Verma module Six operations Shapiro's lemma Tensor-hom adjunction Ring homomorphism Scalar extension Induced module
is Wikipage redirect of	Restriction of scalars Extension of scalars Coinduced module Scalar extension Induced module

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