On weak (σ, δ)-rigid rings over Noetherian rings

Vijay Kumar Bhat, Pradeep Singh, Sunny Sharma
2020 Acta Universitatis Sapientiae: Mathematica  
AbstractLet R be a Noetherian integral domain which is also an algebra over ℚ (ℚ is the field of rational numbers). Let σ be an endo-morphism of R and δ a σ-derivation of R. We recall that a ring R is a weak (σ, δ)-rigid ring if a(σ(a)+ δ(a)) ∈ N(R) if and only if a ∈ N(R) for a ∈ R (N(R) is the set of nilpotent elements of R). With this we prove that if R is a Noetherian integral domain which is also an algebra over ℚ, σ an automorphism of R and δ a σ-derivation of R such that R is a weak (σ,
more » ... at R is a weak (σ, δ)-rigid ring, then N(R) is completely semiprime.
doi:10.2478/ausm-2020-0001 fatcat:g2237p6nqjgvlbzmzrgtj7zjfi