Inertial subalgebras of algebras possessing finite automorphism groups

Journal of the Australian Mathematical Society

Nicholas S. Ford¹ 

关键词: primary 16 A 48;    16 A 16;    secondary 16 A 74;    13H99;   

DOI  :  10.1017/S1446788700012295

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.

【 授权许可】

Unknown