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

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2013

Key Words:

Author NameUniversity of Author

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Abstract (2. Language): 
Let R be a ring and  an endomorphism of R. Recall that R is said to be a (∗)-ring if a(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 -rigid ring if a(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 (∗)-ring and a weak -rigid ring. We also give a necessary and sufficient condition for a Noetherian ring to be a weak -rigid ring. Let  be an endomorphism of a ring R. Then  can be extended to an endomorphism (say ) of R[x;]. With this we show that if R is a Noetherian ring and  an automorphism of R, then R is a weak -rigid ring if and only if R[x;] is a weak -rigid ring.
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  • 1
59-65
  • English

REFERENCES

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