SUBRINGS OF R[X] FIXED BY R-AUTOMORPHISMS

被引：0

作者：

Richmond, Bettina ^{[1
]}

Sandor, Bryan ^{[2
]}

机构：

[1] Western Kentucky Univ, Dept Math, Bowling Green, KY 42101 USA

[2] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2012年 / 40卷 / 11期

关键词：

Invariant subring; Polynomial ring; R-automorphism;

D O I：

10.1080/00927872.2011.607876

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring with identity and let R [X] be the polynomial ring over R in one indeterminate X. Let G (R) denote the group of R-automorphisms of R [X] and B (R) subset of G (R) the subgroup of R-automorphisms mapping X to a linear polynomial. For any subset S of G (R), R [X](S) denotes the subring of R [X] fixed by the elements of S. In 1984, Dowlen showed that if R is assumed to be commutative, then R [X](G(R)) = R [X](B(R)). We establish the analogous result for noncommutative rings R and give some generalizations and applications.

引用

页码：4276 / 4282

页数：7