Rigid Ideals and Radicals of Ore Extensions

• 来源期刊: 代数集刊(英文版)
• 关键词: rigid endomorphisms rigid ideals prime and upper nil radicals Ore extensions
• 年，卷（期）: 2005,（3）
• 页码范围: 399-412
• 页数: 14页
• 语种: 英文

摘要

For an endomorphism σ of a ring R, Krempa called σ a rigid endomorphism if aσ(a) = 0 implies a= 0 for a ∈ R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the σ-rigid property of a ring R to an ideal of R. For a σ-ideal Ⅰ of a ring R, we call Ⅰ a σ-rigid ideal if aσ(a) ∈Ⅰ implies a ∈Ⅰ for a ∈ R. We characterize σ-rigid ideals and study related properties. The connections of the prime radical and the upper nil radical of R with the prime radical and the upper nil radical of the Ore extension R[x; σ, δ], respectively, are also investigated.