|
|
|
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
ring adjunction
|
(Definition)
|
|
"ring adjunction" is owned by pahio.
|
|
(view preamble)
Cross-references: Eisenstein integers, Gaussian integers, multiplications, subtractions, additions, expressions, indeterminate, polynomial ring, subring, ring, extension, commutative ring
There are 2 references to this entry.
This is version 13 of ring adjunction, born on 2004-05-27, modified 2008-03-08.
Object id is 5874, canonical name is RingAdjunction.
Accessed 1697 times total.
Classification:
| AMS MSC: | 13B02 (Commutative rings and algebras :: Ring extensions and related topics :: Extension theory) | | | 13B25 (Commutative rings and algebras :: Ring extensions and related topics :: Polynomials over commutative rings) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
![$ R[\alpha]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img8.png "$ R[\alpha]$"){kind=small}
![$ R[\alpha]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img9.png "$ R[\alpha]$"){kind=small}
![$\displaystyle R[\alpha] = \{f(\alpha)\mid \, f(X)\in R[X]\},$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img13.png "$\displaystyle R[\alpha] = \{f(\alpha)\mid \, f(X)\in R[X]\},$"){kind=small}
![$ R[X]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img14.png "$ R[X]$"){kind=small}
![$ R[\alpha]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img16.png "$ R[\alpha]$"){kind=small}
![$ R[X]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img19.png "$ R[X]$"){kind=small}
![$ \mathbb{Z}[i]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img20.png "$ \mathbb{Z}[i]$"){kind=small}
![$ \mathbb{Z}[\frac{-1+i\sqrt{3}}{2}]$](http://images.planetmath.org:8080/cache/objects/5874/l2h/img21.png "$ \mathbb{Z}[\frac{-1+i\sqrt{3}}{2}]$"){kind=small}