ON S-NOETHERIAN RINGS.

Let R be a commutative ring and S ⊆ R a given multiplicative set. Let (M, ≤) be a strictly ordered monoid satisfying the condition that 0 ≤ m for every m ∈ M. Then it is shown, under some additional conditions, that the generalized power series ring [[RM' ≤]] is S-Noetherian if and only if R is S-Noetherian and M is finitely generated. [ABSTRACT FROM AUTHOR]