PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Medium Entry average rating: High
skew polynomial ring (Definition)

If $ (\sigma, \delta)$ is a left skew derivation on $ R$, then we can construct the (left) skew polynomial ring $ R[\theta;\sigma,\delta]$, which is made up of polynomials in an indeterminate $ \theta$ and left-hand coefficients from $ R$, with multiplication satisfying the relation

$\displaystyle \theta \cdot r = \sigma(r) \cdot \theta + \delta(r)$
for all $ r$ in $ R$.



"skew polynomial ring" is owned by antizeus.
(view preamble)

View style:

Log in to rate this entry.
(view current ratings)

Cross-references: relation, multiplication, coefficients, indeterminate, polynomials, skew derivation
There are 2 references to this entry.

This is version 2 of skew polynomial ring, born on 2001-10-19, modified 2003-09-20.
Object id is 373, canonical name is SkewPolynomialRing.
Accessed 2444 times total.

Classification:
AMS MSC16S36 (Associative rings and algebras :: Rings and algebras arising under various constructions :: Ordinary and skew polynomial rings and semigroup rings)

Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy
Hmmm..... interesting... by patrickwonders on 2002-06-02 10:32:42
In Beachy's book _Introductory_Lectures_on_
_Rings_and_Modules_, he defines the skew
polynomial ring as you did except without
the derivation. Later, he adds the derivation
to form a ``derivation of a skew polynomial ring''.

That seemed more natural to me....
[ reply | up ]

Interact
post | correct | update request | add derivation | add example | add (any)