In this paper, we consider the behavior of polynomial rings over generalized quasi-Baer rings and show that the generalized quasi-Baer condition on a ring R is preserved by many polynomial extensions.
A ring with identity is generalized quasi-Baer if for any ideal I of R, the right annihilator of I n is generated by an idempotent for some positive integer n, depending on I. We study the generalized quasi-Baerness of R[x; σ; δ] over a generalized quasi-Baer ring R where σ is an automorphism of R.
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