About: Galois ring

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In mathematics, Galois rings are a type of finite commutative rings which generalize both the finite fields and the rings of integers modulo a prime power. A Galois ring is constructed from the ring similar to how a finite field is constructed from . It is a Galois extension of , when the concept of a Galois extension is generalized beyond the context of fields.

Attributes	Values
rdfs:label	Galois ring (en)
rdfs:comment	In mathematics, Galois rings are a type of finite commutative rings which generalize both the finite fields and the rings of integers modulo a prime power. A Galois ring is constructed from the ring similar to how a finite field is constructed from . It is a Galois extension of , when the concept of a Galois extension is generalized beyond the context of fields. (en)
dct:subject	Finite rings
Wikipage page ID	46588961 (xsd:integer)
Wikipage revision ID	1118813620 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime power Primitive polynomial (field theory) Principal ideal Root of unity Finite rings Monic polynomial Unit (ring theory) Quotient ring Subring Commutative ring Évariste Galois Maximal ideal Galois extension Galois group Irreducible polynomial Linear code Local ring Cyclic group Field (mathematics) Finite field Fixed point (mathematics) Characteristic (algebra) Coding theory Direct product of groups Automorphism group Wolfgang Krull Finite ring Multiplicative group of integers modulo n Residue field Frobenius automorphism Ring of integers modulo n Primitive root of unity Hensel lifting
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=F_A7DQAAQBAJ https://books.google.com/books%3Fid=H0mAM-Zr0HAC http://www.numdam.org/item%3Fid=CM_1969__21_2_195_0
sameAs	Galois ring Galois ring
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist
has abstract	In mathematics, Galois rings are a type of finite commutative rings which generalize both the finite fields and the rings of integers modulo a prime power. A Galois ring is constructed from the ring similar to how a finite field is constructed from . It is a Galois extension of , when the concept of a Galois extension is generalized beyond the context of fields. Galois rings were studied by Krull (1924), and independently by Janusz (1966) and by Raghavendran (1969), who both introduced the name Galois ring. They are named after Évariste Galois, similar to Galois fields, which is another name for finite fields. Galois rings have found applications in coding theory, where certain codes are best understood as linear codes over using Galois rings GR(4, r). (en)
prov:wasDerivedFrom	wikipedia-en:Galois_ring?oldid=1118813620&ns=0
page length (characters) of wiki page	10450 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Galois_ring
is Link from a Wikipage to another Wikipage of	GR Linear code List of things named after Évariste Galois Finite ring
is Wikipage disambiguates of	GR
is foaf:primaryTopic of	wikipedia-en:Galois_ring

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