Skew Polynomial Rings over Weak sigma-rigid Rings and sigma(*)-rings

Authors

  • Vijay Bhat SMVD UNIVERSITY
  • Neetu Kumari
  • Smarti Gosani

Keywords:

Automorphism, $\sigma(*)$-ring, weak $\sigma$-rigid ring, 2-primal ring

Abstract

Let R be a ring and σ an endomorphism of R. Recall that R is said to be a σ(∗)-ring if aσ(a) ∈ P(R) implies a ∈ P(R) for a ∈ R, where P(R) is the prime radical of R. We also recall that R is said to be a weak σ-rigid ring if aσ(a) ∈ N(R) if and only if a ∈ N(R) for a ∈ R, where N(R) is the set of nilpotent elements of R.

In this paper we give a relation between a σ(∗)-ring and a weak σ-rigid ring. We also give a necessary and sufficient condition for a Noetherian ring to be a weak σ-rigid ring. Let σ be an endomorphism of a ring R. Then σ can be extended to an endomorphism (say σ) of R[x;σ]. With this we show that if R is a Noetherian ring and σ an automorphism of R, then R is a weak σ-rigid ring if and only if R[x;σ] is a weak σ-rigid ring. 

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Published

2013-01-23

Issue

Section

Functional Analysis

How to Cite

Skew Polynomial Rings over Weak sigma-rigid Rings and sigma(*)-rings. (2013). European Journal of Pure and Applied Mathematics, 6(1), 59-65. https://ejpam.com/index.php/ejpam/article/view/1594

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