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special notations in algebra
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(Topic)
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![$ [G\!:\!H]$](http://images.planetmath.org:8080/cache/objects/6955/l2h/img1.png "$ [G\!:\!H]$") , index of a subgroup  in the group  -
 ,  is a normal subgroup of 
 , quotient group of  with respect to the normal subgroup   or  , quotient ring or difference ring of  with respect to the ideal  -
 , center of the group 
![$ R[G]$](http://images.planetmath.org:8080/cache/objects/6955/l2h/img16.png "$ R[G]$") , group ring of the group  over the ring  ![$ R[\alpha]$](http://images.planetmath.org:8080/cache/objects/6955/l2h/img19.png "$ R[\alpha]$") , simple ring adjunction , simple field adjunction , localization of the ring  at  -
 , local ring  with its maximal ideal
 , a left  -module   , a right  -module   , field extension where  is an extension field of  ![$ [K\!:\!k]$](http://images.planetmath.org:8080/cache/objects/6955/l2h/img36.png "$ [K\!:\!k]$") , degree of the field extension  -
 , algebraic closure of a field 
-
 or
 , left ideal of the ring  generated by  , ..., 
-
 , isomorphism between the systems  and 
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"special notations in algebra" is owned by Wkbj79. [ full author list (6) | owner history (1) ]
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| Other names: |
notations in algebra |
This object's parent.
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Cross-references: left ideal, field, algebraic closure, extension field, field extension, right, maximal ideal, local ring, localization, field adjunction, ring adjunction, ring, group ring, center, ideal, quotient ring, quotient group, normal subgroup, group, subgroup
There are 2 references to this entry.
This is version 18 of special notations in algebra, born on 2005-04-17, modified 2007-05-30.
Object id is 6955, canonical name is SpecialNotationsInAlgebra.
Accessed 2730 times total.
Classification:
| AMS MSC: | 08A99 (General algebraic systems :: Algebraic structures :: Miscellaneous) |
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Pending Errata and Addenda
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