Algebraically closed noncommutative polynomial rings
作者:
Kirby C. Smith,
期刊:
Communications in Algebra
(Taylor Available online 1977)
卷期:
Volume 5,
issue 4
页码: 331-346
ISSN:0092-7872
年代: 1977
DOI:10.1080/00927877708822175
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
Let R be a noncommutative polynomial ring over the division ring K where K has center F. Then R = K[x,σ,D]where σ is a monomorphism of K and D is a σ-derivaton K. R is called dimension finite if (K: Fσ)<∞ and (K: FD)<∞ where Fσis the subfield of F fixed under σand FDis the subfied of F of D-constants. R is algebraically closed if every nonconstant polynomial in Rfactors completely into linear factors. The algebraically closed dimension finite polynomial rings are determined. s done by reducing the problem to two classes: skew polynomial rings and differential polynomial rings. Examples algebraically closed polynomial rings which are not dimensfinite are given.
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