【摘 要】
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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 rigi
【机 构】
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Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University, Seoul 130-
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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.
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