Grothendieck group of finitely generated projective modules
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:K_0_group
|
| gptkbp:built |
group completion of the monoid of isomorphism classes of finitely generated projective modules
|
| gptkbp:category |
abelian group
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| gptkbp:defines |
The abelian group generated by isomorphism classes of finitely generated projective modules over a ring, with relations [P⊕Q]=[P]+[Q].
|
| gptkbp:dependsOn |
gptkb:King
|
| gptkbp:field |
gptkb:algebra
gptkb:algebraic_K-theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Grothendieck group of finitely generated projective modules
|
| gptkbp:introduced |
gptkb:Alexander_Grothendieck
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| gptkbp:notation |
K_0(R)
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| gptkbp:property |
K_0 of a field is isomorphic to the integers
K_0 of a local ring is isomorphic to the integers functorial in the ring K_0 of a semisimple ring is a free abelian group of rank equal to the number of simple modules |
| gptkbp:relatedTo |
gptkb:K-theory
gptkb:Grothendieck_group projective module |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:topology gptkb:algebraic_K-theory |
| gptkbp:bfsParent |
gptkb:K_0_functor
|
| gptkbp:bfsLayer |
7
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