S-Noetherian Rings of the Forms 𝒜[X] and 𝒜[[X]] |
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| Authors: | Hamed Ahmed Hizem Sana |
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| Institution: | 1. Department of Mathematics, Faculty of Sciences , University of Monastir , Monastir , Tunisia hamed.ahmed@hotmail.fr;3. Department of Mathematics, Faculty of Sciences , University of Monastir , Monastir , Tunisia |
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| 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 𝒜X] (respectively, 𝒜X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A i for each i ∈ ?. In this paper, we give necessary and sufficient conditions for the rings 𝒜X] and 𝒜X]] to be S ? Noetherian. |
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| Keywords: | Formal power series rings Polynomial ring S-Noetherian |
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