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Theoretical analysis uncovers algebraic behaviors of the filter limit in commutative rings, highlighting fundamental connections to the ultraproduct construction.
In this article, we investigate various algebraic properties of the ℱ-limit, where ℱ is a filter on the set of natural numbers ℕ. More precisely, we study its behavior under ideal-theoretic operations, as well as its interaction with structural properties of commutative rings and its connection to the ultraproduct construction.
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Oudika et al. (2026) studied this question.
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