Abstract
Let 𝒜 = (A n ) n≥0 be an ascending chain of commutative rings with identity, S ⊆ A 0 a multiplicative set of A 0, and let 𝒜[X] (respectively, 𝒜[[X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A i for each i ∈ ℕ. In this paper, we give necessary and sufficient conditions for the rings 𝒜[X] and 𝒜[[X]] to be S − Noetherian.
ACKNOWLEDGMENT
The authors would like to thank the referee for his/her careful considerations.
Notes
Communicated by S. Bazzoni.