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ABSTRACT A commutative ring R with identity is called S-Noetherian, where is a given multiplicative set, if for each ideal I of R, for some and some finitely generated ideal J. Using this concept, we tie together several different known results. For instance, the fact that is a Noetherian ring whenever R is so, and that is Noetherian whenever for each nonzero element d of the domain D areboth consequences of the following result: If R is an S-Noetherian ring, then so is , provided for each where S consists of nonzerodivisors.
Anderson et al. (Tue,) studied this question.