Abstract
Let ๐ = (A n ) nโฅ0 be an ascending chain of commutative rings with identity, S โ A 0 a multiplicative set of A 0, and let ๐[X] (respectively, ๐[[X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A i for each i โ โ. In this paper, we give necessary and sufficient conditions for the rings ๐[X] and ๐[[X]] to be S โ Noetherian.
ACKNOWLEDGMENT
The authors would like to thank the referee for his/her careful considerations.
Notes
Communicated by S. Bazzoni.