### 2-primal weak (σ,δ)-rigid rings

#### Abstract

For a ring R, an endomorphism σ of R and δ a σ-derivation of R, we introduce a weak (σ,δ)-rigid ring, which generalizes the notion of (σ,δ)-rigid rings and investigate its properties. Moreover, we state and prove a necessary and sufficient condition for a weak (σ,δ)-rigid ring to be a (σ,δ)-rigid ring. We prove that a (σ,δ)-ring is a weak (σ,δ)-rigid ring and conversely that the prime radical of a weak(σ,δ)-rigid ring is a (σ,δ)-ring. We also find a relation between minimal prime ideals and completely prime ideals of a ring R, where R is a (σ,δ)-ring and R is a 2-primal weak (σ,δ)-rigid ring.

**Published:**2014-05-23

**How to Cite this Article:**M. Abrol, V. K. Bhat, 2-primal weak (σ,δ)-rigid rings, Algebra Lett., 2014 (2014), Article ID 1 Copyright © 2014 M. Abrol, V. K. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Algebra Letters

ISSN 2051-5502

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